I review our latest off-axis holographic compression techniques for quantitative phase microscopy of dynamic cells. Offaxis holography allows quantitative acquisition of live cells without staining, by reconstructing their quantitative phase profile from a single camera exposure. In this technique, one of the interfering beams is slightly tilted relative to the other beam, creating separation of the field intensity from the two conjugate wave front terms in the spatial-frequency domain. We showed that this encoding leaves a lot of empty space in the spatial-frequency domain, into which additional information can be compressed. This compression can be done using optical multiplexing of up to six complex wave fronts into a single camera plane, where each pair of sample and reference beams creates an off-axis hologram with a different interference fringe direction that positions the wave fronts in the spatial frequency domain without overlapping with any other term. This new holographic compression approach is useful for various applications, with focus on quantitative phase acquisition of fast cellular dynamics, including imaging cells during rapid flow. I present several experimental systems that implement this holographic compression approach, and review various applications.