Time-dependent two-level models have been an important element in physics, and in particular in quantum optics since 1930's. We review the basics of these models and focus on the dynamics induced by off-resonant zero-area pulses by using a Sech-Tanh pulse model as an example. We show that the final transition probability for this model is described accurately by the Dykhne-Davis-Pechukas approach for certain parameter regions. Finally, we note the potential of such zero area pulse models in quantum control and quantum information.