Flash memories have become the main type of non-volatile memories. They are widely used in mobile, embedded and mass-storage devices. Flash memories store data in floating-gate cells, where the amount of charge stored in cells – called cell levels – is used to represent data. To reduce the level of any cell, a whole cell block (about 106 cells) must be erased together and then reprogrammed. This operation, called block erasure, is very costly and brings significant challenges to cell programming and rewriting of data. To address these challenges, rank modulation and rewriting codes have been proposed for reliably storing and modifying data. However, for these new schemes, many problems still remain open. In this work, we study error-correcting rank-modulation codes and rewriting codes for flash memories. For the rank modulation scheme, we study a family of one- error-correcting codes, and present efficient encoding and decoding algorithms. For rewriting, we study a family of linear write-once memory (WOM) codes, and present an effective algorithm for rewriting using the codes. We analyze the performance of our solutions for both schemes.