The gain dynamics of bulk laser amplifiers is discussed on the basis of simple rate equations, and comparison is made with experimental pump-and-probe measurements employing ultrashort optical pulses. The rate equation model is derived from semi-classical density matrix equations, and is analyzed in different limiting cases, i.e., an adiabatic limit corresponding to nonlinear gain in laser diodes, a small-signal limit yielding an analytical repsonse function, and a strong-signal regime, where numerical simulations are carried out.