The photoacid dynamics of fluorescent proteins include both electronic excited- and ground-state mechanisms of proton transfer. The associated characteristic timescales of these reactions range over many orders of magnitude, and the tunneling, barrier crossing, and relevant thermodynamics have in certain cases been linked to coherent nuclear motion. We review the literature and summarize the experiments and theory that demonstrate proton tunneling in the electronic ground state of the green fluorescent protein (GFP). We also discuss the excited-state proton-transfer reaction of GFP that takes place on the picosecond timescale. Although this reaction has been investigated using several vibrational spectroscopic methods, the interpretation remains unsettled. We discuss recent advances as well as remaining questions, in particular those related to the vibrational mode couplings that involve low-frequency modulations of chromophore vibrations on the timescale of proton transfer.