The rise to power of the Olympians was not an easy one, in fact, under Zeus' leadership the young Gods had many toils and troubles to overcome before They became the dominant force in the universe. Two of those hurdles were the Gigantomachy and the Titanomachy, two events that were first depicted as separate events but became more entwined as the years went on. Because there had been some confusion between who the Gigantes were and who the Titanes were, I'm going to do a short introduction to both today.

The Titanes came first, after the Protogenoi (Πρωτογενοι). The Protogenoi are the First Born Deities of the Hellenic Kosmos. They are the building blocks of the universe, primordial Deities. Examples include, Gaea, Nyx, Eros, and Ouranos. Then came the Titanes Gods (Τιτανες Θεοι), or Titans. This generation included deities like Hyperion, Rhea, Phoebe, Themis, and Prometheus. We label the generation after Them 'Titanes' as well, and this generation includes Helios, Hekatê, Mêtis, and the Mousai. The Olypic Gods came after.

The Gigantes were a tribe of one hundred Giants born of Gaia. Some say their father was Tartaros, others that they were born from the blood of the castrated Ouranos. They aren't considered Gods, but fall under the label of 'monster', like the Gorgons and the Hekatonkheires. Hesiod, in his Theogony describes the birth of the Gigantes:

"Then the son from his ambush stretched forth his left hand and in his right took the great long sickle with jagged teeth, and swiftly lopped off his own father's members and cast them away to fall behind him. And not vainly did they fall from his hand; for all the bloody drops that gushed forth Earth received, and as the seasons moved round she bare the strong Erinyes and the great Giants with gleaming armour, holding long spears in their hands and the Nymphs whom they call Meliae all over the boundless earth." [177]

Again in the Theogony, we find a description of the Titanomachy:
 
"But the son of Cronos and the other deathless gods whom rich-haired Rhea bare from union with Cronos, brought them up again to the light at Earth's advising. For she herself recounted all things to the gods fully, how that with these they would gain victory and a glorious cause to vaunt themselves. For the Titan gods and as many as sprang from Cronos had long been fighting together in stubborn war with heart-grieving toil, the lordly Titans from high Othyrs, but the gods, givers of good, whom rich-haired Rhea bare in union with Cronos, from Olympus. So they, with bitter wrath, were fighting continually with one another at that time for ten full years, and the hard strife had no close or end for either side, and the issue of the war hung evenly balanced. But when he had provided those three with all things fitting, nectar and ambrosia which the gods themselves eat, and when their proud spirit revived within them all after they had fed on nectar and delicious ambrosia, then it was that the father of men and gods spoke amongst them:
 
`Hear me, bright children of Earth and Heaven, that I may say what my heart within me bids. A long while now have we, who are sprung from Cronos and the Titan gods, fought with each other every day to get victory and to prevail. But do you show your great might and unconquerable strength, and face the Titans in bitter strife; for remember our friendly kindness, and from what sufferings you are come back to the light from your cruel bondage under misty gloom through our counsels.'
 
So he said. And blameless Cottus answered him again: `Divine one, you speak that which we know well: nay, even of ourselves we know that your wisdom and understanding is exceeding, and that you became a defender of the deathless ones from chill doom. And through your devising we are come back again from the murky gloom and from our merciless bonds, enjoying what we looked not for, O lord, son of Cronos. And so now with fixed purpose and deliberate counsel we will aid your power in dreadful strife and will fight against the Titans in hard battle.'
 
So he said: and the gods, givers of good things, applauded when they heard his word, and their spirit longed for war even more than before, and they all, both male and female, stirred up hated battle that day, the Titan gods, and all that were born of Cronos together with those dread, mighty ones of overwhelming strength whom Zeus brought up to the light from Erebus beneath the earth. An hundred arms sprang from the shoulders of all alike, and each had fifty heads growing upon his shoulders upon stout limbs. These, then, stood against the Titans in grim strife, holding huge rocks in their strong hands. And on the other part the Titans eagerly strengthened their ranks, and both sides at one time showed the work of their hands and their might. The boundless sea rang terribly around, and the earth crashed loudly: wide Heaven was shaken and groaned, and high Olympus reeled from its foundation under the charge of the undying gods, and a heavy quaking reached dim Tartarus and the deep sound of their feet in the fearful onset and of their hard missiles. So, then, they launched their grievous shafts upon one another, and the cry of both armies as they shouted reached to starry heaven; and they met together with a great battle-cry.
 
Then Zeus no longer held back his might; but straight his heart was filled with fury and he showed forth all his strength. From Heaven and from Olympus he came forthwith, hurling his lightning: the bold flew thick and fast from his strong hand together with thunder and lightning, whirling an awesome flame. The life-giving earth crashed around in burning, and the vast wood crackled loud with fire all about. All the land seethed, and Ocean's streams and the unfruitful sea. The hot vapour lapped round the earthborn Titans: flame unspeakable rose to the bright upper air: the flashing glare of the thunder- stone and lightning blinded their eyes for all that there were strong. Astounding heat seized Chaos: and to see with eyes and to hear the sound with ears it seemed even as if Earth and wide Heaven above came together; for such a mighty crash would have arisen if Earth were being hurled to ruin, and Heaven from on high were hurling her down; so great a crash was there while the gods were meeting together in strife. Also the winds brought rumbling earthquake and duststorm, thunder and lightning and the lurid thunderbolt, which are the shafts of great Zeus, and carried the clangour and the warcry into the midst of the two hosts. An horrible uproar of terrible strife arose: mighty deeds were shown and the battle inclined. But until then, they kept at one another and fought continually in cruel war.
 
And amongst the foremost Cottus and Briareos and Gyes insatiate for war raised fierce fighting: three hundred rocks, one upon another, they launched from their strong hands and overshadowed the Titans with their missiles, and buried them beneath the wide-pathed earth, and bound them in bitter chains when they had conquered them by their strength for all their great spirit, as far beneath the earth to Tartarus. For a brazen anvil falling down from heaven nine nights and days would reach the earth upon the tenth: and again, a brazen anvil falling from earth nine nights and days would reach Tartarus upon the tenth. Round it runs a fence of bronze, and night spreads in triple line all about it like a neck-circlet, while above grow the roots of the earth and unfruitful sea. There by the counsel of Zeus who drives the clouds the Titan gods are hidden under misty gloom, in a dank place where are the ends of the huge earth. And they may not go out; for Poseidon fixed gates of bronze upon it, and a wall runs all round it on every side. There Gyes and Cottus and great-souled Obriareus live, trusty warders of Zeus who holds the aegis.
 
And there, all in their order, are the sources and ends of gloomy earth and misty Tartarus and the unfruitful sea and starry heaven, loathsome and dank, which even the gods abhor." [617 - 744]
As for the Gigantomachy, Pseudo-Apollodorus' Bibliotheca has a beautiful account of it:

"Now because of her anger over the Titanes, Ge gave birth to the Gigantes, Ouranos was the father. These creatures were unsurpassed in the size of their bodies and unconquerable by virtue of their power. They were frightening in appearance, with long hair that swept down from their heads and chins, and serpent-scales covering their lower limbs. Some say that they were born in Phlegrae, others in Pallene. They would hurl rocks and flaming oak trees at the sky.

 The greatest of them were Porphyrion and Alkyoneus, who was in fact immortal provided he did his fighting in the land where he was born. It was Alkyoneus who drove away the cattle of Helios from Erytheia [the Sunset Isle].

 Now there was an oracle among the gods that they themselves would not be able to destroy any of the Gigantes, but would finish them off only with the help of some mortal ally. When Ge (Earth) learned of this, she sought a drug that would prevent their destruction even by mortal hands. But Zeus barred the appearance of Eos, Selene, and Helios, and chopped up the drug himself before Ge could find it.

 Then with Athene's help he called for Herakles to be his ally. Herakles first sent and arrow at Alkyoneus, who by falling to the earth recovered somewhat. Athene advised Herakles to drag him outside of Pallene, which he did, and Alkyoneus thereupon died.

 In the course of the battle Porphyrion rushed against Herakles and also Hera. Zeus instilled him with a passion for Hera, and when he tore her gown and wanted to rape her, she called for help, whereat Zeus hit him with a thunderbolt and Herakles slew him with an arrow. As for the rest, Apollon sent an arrow into the left eye of Ephialtes, Herakles into the right; Dionysos slew Eurytos with his thyrsos; Hekate got Klytios with fire-brands; and Hephaistos killed Mimas by throwing molten iron at him. As Enkelados was fleeing, Athene threw the island of Sikilia (Sicily) in his direction. She stripped the skin off Pallas and used it to protect her own body during the battle. Polybotes was pursued through the sea by Poseidon until he reached Kos. There Poseidon ripped off the part of that island called Nisyros and threw it at him. Hermes, who was wearing the helmet of Haides, killed Hippolytos in the course of the battle, and Artemis killed Aigaion. The Moirai fought with bronze maces and killed Agrios and Thoon, whiles Zeus destroyed the rest by throwing his thunderbolts. Herakles sent arrows into all of them as they lay dying." [34 - 38]

By the time of the Romans (and even the late Hellenes) the two events become largely equated. They are either seen as one struggle, or events become mixed. Not always, but as time went on, it happened more often, and I am sure this is where the modern confusion stems from. In ancient Hellenic times, however, the two races and wars were very distinct and had very different outcomes. Thus ends today's mythology lesson.