In this talk, we discuss coding schemes for data storage systems, including flash memories, racetrack memories, and DNA-based systems. In particular, we present several constrained codes avoiding specific patterns and focus on codes correcting synchronization errors, such as deletions and sticky-insertions. Firstly, we show that constrained codes can be useful for avoiding some potential errors. Especially, we present ICI-free codes for flash memories and locally constrained codes for DNA-based storages. Then, we present several new families codes correcting synchronization errors, including q-ary codes, permutation codes, multi-dimensional codes, and symbol-pair codes and their applications in flash memories, and racetrack memories. Finally, we study several constrained codes avoiding specific set of patterns that can be used to correct synchronization errors in racetrack memories and DNA-based storage systems. A few open questions will be discussed in the end of the talk. This talk is based on joint works with Yeow Meng Chee, Tuvi Etzion, Kees A. Schouhamer Immink, Manabu Hagiwara, Hanmao Kiah, Alexander Vardy, and Eitan Yaakobi.