This dissertation focuses on three types of emerging NVMs, spin-transfer torque RAM (STT-RAM), phase change memory (PCM), and metal-oxide resistive RAM (ReRAM). STT-RAM has been identified as the best replacement of SRAM to build large-scale and low-power on-chip caches and also an energy-efficient alternative to DRAM as main memory. PCM and ReRAM have been considered to be promising technologies for building future large-scale and low-power main memory systems. This dissertation investigates two aspects to facilitate them in next-generation memory system design, architecture-level and application-level perspectives. First, multi-level cell (MLC) STT-RAM based cache design is optimized by using data encoding and data compression. Second, MLC STT-RAM is utilized as persistent main memory for fast and energy-efficient local checkpointing. Third, the commonly used database indexing algorithm, B+tree, is redesigned to be NVM-friendly. Forth, a novel processing-in-memory architecture built on ReRAM based main memory is proposed to accelerate neural network applications.