Processor power constraints have come to the forefront over the last decade, heralded by the stagnation of clock frequency scaling. High-performance core and cache designs often utilize power-hungry techniques to increase parallelism. Conversely, the most energy-efficient designs opt for a serial execution to avoid unnecessary overheads. While both of these extremes constitute one-size-fits-all approaches, a judicious mix of parallel and serial execution has the potential to achieve the best of both high-performing and energy-efficient designs. This dissertation examines such hybrid designs for cores and caches. Firstly, we introduce a novel, hybrid out-of-order/in-order core microarchitecture. Instructions that are steered towards in-order execution skip register allocation, reordering and dynamic scheduling. At the same time, these instructions can interleave on an instruction-by-instruction basis with instructions that continue to benefit from these conventional out-of-order mechanisms. Secondly, this dissertation revisits a hybrid technique introduced for L1 caches, way-prediction, in the context of last-level caches that are larger, have higher associativity, and experience less locality.