Computational neuroscience is focused on uncovering general organizational principles supporting neural activity and behavior; however, uncovering these principles relies on making appropriate comparisons across individuals. This presents a core technical and conceptual challenge, as individuals differ along nearly every relevant dimension: from the number of neurons supporting computation to the exact computation being performed. Similarly in artificial neural networks, multiple initializations of the same architecture—on the same data—may recruit non-overlapping hidden units, complicating direct comparisons of trained networks. In this talk, I will introduce techniques for aligning representations in both brains and in machines. I will argue for the importance of considering alignment methods in developing a comprehensive science at the intersection of artificial intelligence and neuroscience that reflects our shared goal of understanding principles of computation. Finally, I will consider current applications and limitations of these techniques, discussing relevant future directions for this area.