This paper provides a comprehensive overview of floating-body induced transient effects and instabilities in SOI MOSFETs and circuits. The physical mechanisms responsible far various transient effects are clarified through high speed measurements and 2D device simulations. We demonstrate that the well-known sub-threshold kink in static I-V curves of an SOI MOSFET doesn't exist under typical high speed switching conditions. We also show that the drain current of a partially-depleted (PD) SOI MOSFET during switching is not a simple function of external biases but has a significant history dependence (hysteresis) even in the absence of impact ionization at very low power supply voltages. The pulse I-V technique, overcoming self-heating problems, is most suitable for the extraction and calibration of physical and model parameters for charge-based compact SOI device models that are required for accurate modeling of floating-body SOI circuits. Design and process considerations, SOI material quality improvement, lifetime tailoring, bandgap engineering, novel device concepts, and circuit design approaches are outlined to minimize these transient/hysteresis effects.