I will discuss the collective modes that spontaneously emerge in ciliary carpets and fish schools. In both systems, the fluid medium couples the motion of individuals in the group. Flow coupling is dominated by viscous forces in cilia and by inertial interactions in fish. I will show, numerically and analytically in the continuum limit, that the waves that emerge in ciliary carpets are robust to morphological and kinematic perturbations of the ciliated tissues. In fish schools, I will show intermittent collective behavior with back-and-forth switching between schooling and milling, and I will analyze the bifurcations underlying phase transitions by lifting the stochastic dynamics of individual fish onto a Fokker-Planck equation that governs the group dynamics. These problems highlight how structure, activity, and environment interconnect to produce emergent biological function; our work provides a framework for establishing structure-to-function maps across multiple length scales to help understand, probe, and engineer emergent phenomena in biological and biomedical systems.