Abstract: High penetration of grid-connected inverters is changing the forms and roles of resources in power grids. The inverters are required to be functioned like the synchronous generators, which leads to a new form of inverter control-grid-forming control. In this paper, the development of grid-forming control is comprehensively reviewed, including its definition, variants, grid code discussions, demonstration projects and challenges. The characteristics in terms of small-signal stability are compared between the grid-forming control and the conventional grid-following control. Increasing renewable resources are integrated from the remote connection point of the grid, which leads to a greatly concerned issue of weak-grid instability. A simple and effective tuning method is provided to enable the grid-following inverter to connect to an extreme weak grid even at SCR=1. It is revealed that besides grid-forming inverters, a grid-following inverter can achieve satisfactory stability in a weak grid.