Two-dimensional graphene monolayers and bilayers exhibit fascinating electrical transport behaviors. Using infrared spectroscopy, we find that they also have strong interband transitions and that their optical transitions can be substantially modified through electrical gating, much like electrical transport in field-effect transistors. This gate dependence of interband transitions adds a valuable dimension for optically probing graphene band structure. For a graphene monolayer, it yields directly the linear band dispersion of Dirac fermions, whereas in a bilayer, it reveals a dominating van Hove singularity arising from interlayer coupling. The strong and layer-dependent optical transitions of graphene and the tunability by simple electrical gating hold promise for new applications in infrared optics and optoelectronics.