Neutrinos are among the most abundant particles in the universe. The discovery that they have nonzero masses has raised a number of very interesting questions about them, and about their connections to other areas of physics and to cosmology. After briefly reviewing what has been learned about the neutrinos so far, we will identify the major open questions, explain why they are interesting, and discuss ideas and plans for answering them through future experiments. We will highlight a particularly intriguing question: Are neutrinos the key to understanding why the universe contains  matter but almost no antimatter, making it safe for life?