Continuous-variable (CV) quantum systems underpin free-space and fiber-optic communication links as well as photonic and phononic platforms for computation and simulation. Like all quantum systems, CV systems require error correction to counteract noise, yet CV quantum error correction remains relatively underexplored because conventional discrete-variable coding theory offers limited guidance. I present several new classes of CV error-correcting codes and associated fault-tolerant gadgets that extend beyond discrete-variable approaches by exploiting both the energy per mode (“depth”) and the number of modes (“breadth”) of the system’s Hilbert space.