Amylin receptors (AMYRs) are heterodimers of the calcitonin (CT) receptor (CTR) and one of three receptor activity-modifying proteins (RAMPs), AMY1R, AMY2R, and AMY3R. Selective AMYR agonists and dual AMYR/CTR agonists are being developed as obesity treatments; however, the molecular basis for peptide binding and selectivity is unknown. We determined the structure and dynamics of active AMYRs with amylin, AMY1R with salmon CT (sCT), AMY2R with sCT or human CT (hCT), and CTR with amylin, sCT, or hCT. The conformation of amylin-bound complexes was similar for all AMYRs, constrained by the RAMP, and an ordered midpeptide motif that we call the bypass motif. The CT-bound AMYR complexes were distinct, overlapping the CT-bound CTR complexes. Our findings indicate that activation of AMYRs by CT-based peptides is distinct from their activation by amylin-based peptides. This has important implications for the development of AMYR therapeutics.