See בראשית ט:יח-כט! Immediately after Noach's family exits the ark, there is a most peculiar incident in which Noach gets drunk, Cham does something very bad, and Shem and Yefet try to fix Cham's sin. Noach curses Cana'an (Cham's son) and blesses Shem and Yefet.
To begin with, where did Cana'an come from? We are told (שם ז:יג) that only Noach, his three sons, and their wives entered the ark. (There is one answer staring us in the face, namely that Cham broke the ban on relations with his wife during the flood, and Cana'an born in the ark from that sin. This may explain some of the later questions.)
The Torah tells us that Cham "saw his father's nakedness." How does this warrant the eternal curse on Cana'an, which Noach gives in פסוק כה? Furthermore, why does Noach curse Cana'an for his father Cham's action? Is this related to the fact that the Torah constantly refers to Cham as אבי כנען, Cana'an's father? (Note: very often, somebody is called אבי something because he was the founder or creator of it, as in בראשית ד:כ-כא. Perhaps Cham was somehow אבי כנען in this sense, aside from any biological relation. Thus, Noach viewed Cana'an Cham's disciple in wickedness and cursed him accordingly.)
In פרק י, we are told of how the famous seventy nations, seventy descendants of Noach, spread out to inhabit the earth. The Torah gives borders that divide the earth into three sections, one for the nations of each son of Noach. Were these borders assigned by Noach, assigned by Hashem, or grabbed by each son? This question is particularly significant, because a simple understanding of the פסוקים here indicates that Eretz Yisrael was within the borders of Cham (בראשית י:יט). However, Bnei Yisrael are descended from Shem, implying that Eretz Yisrael wasn't originally given to Bnei Yisrael (עיין רמב"ן שם, ורש"י שם יב:ו). Does this mean that Hashem initially planned for there to be no chosen people or chosen land, so He didn't care who lived in Israel? Alternatively, did Hashem plan already at this point that the land would start out with another nation, because He specifically wanted the Jews to have the experience of conquering Eretz Yisrael from pagan nations?