We present a review of our recent studies of Bias Temperature Instability (BTI) in Metal-Oxide-Semiconductor Field-Effect-Transistors (MOSFETs) fabricated with different material systems, highlighting the reliability opportunities and challenges of each novel device family. We discuss first the intrinsic reliability improvement offered by SiGe and Ge p-channel technologies, if a Si cap is used to passivate the channel, in order to fabricate a standard SiO2/HfO2 gate stack. We focus on SiGe gate stack optimizations for maximum BTI reliability, and on a simple physics-based model able to reproduce the experimental trends. This model framework is then used to understand the suboptimal BTI reliability and excessive time-dependent variability induced by oxide defect charging in different high-mobility channel gate stacks, such as Ge/GeOx/high-k and InGaAs/high-k. Finally we discuss how to pursue a reduction of charge trapping in alternative material systems in order to boost the device reliability and minimize time-dependent variability.