When we talk with each other, we do much more than exchange words. We take turns with short gaps or overlaps, we gesture, and we tend to use similar word choices, sentence structures, and gestures. It has long been known that this mirroring or alignment of language helps communication run smoothly, and that people automatically and strategically repeat each other's words in conversation. What is far less understood is whether the same holds for gesture. This dissertation investigates why we repeat each other's gestures in conversation and how alignment in words and alignment in gestures are connected. To tackle these questions, it analyzes existing recordings of people communicating about novel objects, builds and validates a new computational framework for measuring how similar two gestures look, and conducts an experiment to test what drives gestural alignment in the first place. Taken together, the studies show that people repeat each other's word choices and gestures throughout their conversations, that people are automatically influenced to produce gestures with similar meaning, and that alignment in gestures is closely tied to alignment in word choices. Overall, alignment is a natural part of how we talk, and understanding why it happens and how it helps conversation sheds light on how we use language and understand each other.