Book excerpt: Non-volatile memories are an emerging storage technology with wide applica- tions in many important areas. This study focuses on new storage techniques for flash memories and phase-change memories. Flash memories are currently the most widely used type of non-volatile memory, and phase-change memories (PCMs) are the most promising candidate for the next-generation non-volatile memories. Like magnetic recording and optical recording, flash memories and PCMs have their own distinct properties, which introduce very interesting data storage problems. They include error correction, cell programming and other coding problems that affect the reliability and efficiency of data storage. Solutions to these problems can signifi- cantly improve the longevity and performance of the storage systems based on flash memories and PCMs. In this work, we study several new techniques for data storage in flash memories and PCMs. First, we study new types of error-correcting codes for flash memories 0́3 called error scrubbing codes 0́3that correct errors by only increasing cell levels. Error scrubbing codes can correct errors without the costly block erasure operations, and we show how they can outperform conventional error-correcting codes. Next, we study the programming strategies for flash memory cells, and present an adaptive algorithm that optimizes the expected precision of cell programming. We then study data storage in PCMs, where thermal interference is a major challenge for data reliability. We present two new coding techniques that reduce thermal interference, and study their storage capacities and code constructions.