I will discuss webs for symplectic groups (type C) and orthogonal groups (type O), based on joint work with Elias--Rose--Tatham and Haihan Wu respectively. Our main results give complete sets of generators and relations for the monoidal categories generated by fundamental representations. We also find explicit bases in some special cases. The talk will begin by reviewing the rank 2 symplectic group case, which already appeared in Kuperberg's ``Spiders for rank 2 Lie algebras". Then I will explain how to generalize to higher rank and to the orthogonal setting.