We are active matter. From the subcellular processes occurring within a living cell to the large-scale collective dynamics of human crowds or animal flocks, systems driven far from equilibrium by a sustained flux of energy through its constituents routinely exhibit stunning emergent phenomena that pose fundamental challenges to our understanding of the natural world. I will discuss how paradigmatic phenomena in such active systems can be fruitfully understood by combining tools from soft matter, geometry, and topology, often with surprising consequences. Going beyond pattern formation, I will discuss recent work on deploying control strategies to manipulate active materials and highlight future directions for functional biological and synthetic active systems.