We summarize the results of recent studies of diboson and multiboson production performed on proton-proton collision data from the CMS detector at the LHC. Results discussed include ZZ, W$^\pm$Z, and W$^+$W$^-$ inclusive cross section measurements at $\sqrt{s} = 13$~TeV, as well as measurements of the Z$\gamma\gamma$, W$^\pm\gamma\gamma$, $\gamma\gamma \to $W$^+$W$^-$, and electroweak Z$\gamma + 2$jets and W$^\pm\gamma + 2$jets cross sections at $\sqrt{s} = 8$~TeV. Measurements done at $\sqrt{s} = 8$~TeV are used to place limits on anomalous quartic gauge boson couplings.