This talk is mainly concerned with the convergence rates in homogenization of elliptic and parabolic systems with stratified or locally periodic structures. This kinds of systems have much theoretical significance in homogenization and strong backgrounds in biomechanics and engineering. I will present my recent work jointly with Weisheng Niu on the sharp convergence rate of elliptic systems as well as some interior regularity estimates. Compared to the traditional cases, we took the best advantage of the smoothing operators and overcame a series of special difficulties occurred in our case. Some interesting results in current work on parabolic systems will also be presented briefly.