The renewable energy sources (RESs) dominated power grid is an envisaged infrastructure of the future power system, where the commonly used grid following (GFL) control for grid-tied converters suffers from lacking grid support capability, low stability, etc. Recently, emerging grid forming (GFM) control methods have been proposed to improve the dynamic performance and stability of grid-tied converters. This paper reviews existing GFM control methods for the grid-tied converters and compares them in terms of control structure, grid support capability, fault current limiting, and stability. Considering the impact of fault current limiting strategies, a comprehensive transient stability analysis is provided. In addition, this paper explores the typical applications of GFM converters, such as AC microgrid and offshore wind farm high-voltage direct current (OWF-HVDC) integration systems. Finally, the challenges to the GFM converters in future applications are discussed.