With energy，zoology and environments being paid increasing attention，a photovoltaic（PV） system supplying power directly to a power grid becomes more popular available. This paper focuses on the structure design and control strategies of inverters for the grid-connected PV system. It starts with an examination of the demands requested by the power grid，the PV array and the users for the inverters. Then follows a review to see how these demands are achieved with all sorts of topologies and control strategies of inverters and accordingly the working efficiency and control effect are compared. Also， the background，the fundamentals，the approaches and the main results of evolutionary grid-connected PV inverters are outlined. In the end， several open questions and the state-of-arts of the grid-connected PV inverters are discussed.