Generally, industrial gas turbines (IGT) face transient behavior during start-up, load change, shutdown and variations in ambient conditions. These transient conditions shift engine thermal equilibrium from one steady state to another steady state. In turn, various aero-thermal and mechanical stresses are developed that are adverse for engine's reliability, availability, and overall health. The transient behavior needs to be accurately predicted since it is highly related to low cycle fatigue and early failures, especially in the hot regions of the gas turbine. In the present paper, several critical aspects related to transient behavior and its modeling are reviewed and studied from the point of view of identifying potential research gaps within the context of fault detection and diagnostics (FDD) under dynamic conditions. Among the considered topics are, (i) general transient regimes and pertinent model formulation techniques, (ii) control mechanism for part-load operation, (iii) developing a database of variable geometry inlet guide vanes (VIGVs) and variable bleed valves (VBVs) schedules along with selection framework, and (iv) data compilation of shaft's polar moment of inertia for different types of engine's configurations. This comprehensive literature document, considering all the aspects of transient behavior and its associated modeling techniques will serve as an anchor point for the future researchers, gas turbine operators and design engineers for effective prognostics, FDD and predictive condition monitoring for variable geometry IGT.