Many important client and data-center applications need large memory capacity and high memory bandwidth to achieve their performance and energy efficiency goals. With the increase in data-centered computing, these trends are ever-growing. Hardware memory compression provides a promising direction to increase effective memory capacity and bandwidth without increasing system cost. Unfortunately, previously proposed memory compression solutions face significant challenges with respect to their evaluation methodology, performance, and time-to-market.This dissertation identifies the trade-offs that most influence the performance of compressed main memory. It provides main memory compression solutions for both general purpose CPUs and general purpose GPUs, and evaluates them with holistic and accurate methodology. The dissertation also provides a set of solutions to increase the feasibility of the main memory compression by making it completely transparent to the operating system.Thesis Statement: Hardware main memory compression is a cost-effective solution to the memory capacity wall and can reduce the total cost of ownership of a system. It can be made feasible by designing it with a focus on less data movement and minimal intrusion. This dissertation aims to provide high compression benefits for memory over-commitment phases, while maintaining high performance for the low memory-pressure phases.