Hardy-Rellich type inequalities have broad applications in different fields of analysis and geometry, they have been studied extensively since Hardy’s seminal works one century ago. In this talk, we will revise firstly various first order Hardy inequalities, and point out that most of them can be obtained by a simple and unified equality. This approach permits us to get some new or improved first order Hardy inequalities. We will explain also our approach to obtain higher order Hardy-Rellich type equalities which imply and improve many classical Hardy-Rellich inequalities. This is a joint work with Professor Dong YE at ECNU.