With the increasing penetration rate of renewable energy generation, the stable operation of grid-connected converters with grid-following control as the mainstream has been severely challenged. Therefore, the control technologies of grid-forming converters with active support capability for the power grid and strong stability in the weak power grid have received much attention. However, under the conditions of high penetration rate of renewable energy generation, especially in the terminal weak grid, it is difficult for the grid-connected converters to balance stability, economy, and power grid support performance by using a single grid-following or grid-forming mode control. Based on the complementary characteristics of the two modes, scholars at home and abroad have proposed and studied the grid-following/grid-forming hybrid mode control strategy, to make the grid-connected converters operate stably in the weak power grid, maximize the use of renewable energy, and achieve superior power grid support performance. Starting from the basic control structures of grid-following and grid-forming converters, this paper analyzes the complementary characteristics of the control performance of grid-following and grid-forming converters. On this basis, the hybrid mode control schemes of several different technical routes are sorted out, involving a variety of single-machine hybrid control strategies and multi-machine station-level hybrid control strategies. The technical research idea, principle, advantages, and disadvantages of each scheme are elaborated in detail. Finally, the development of grid-following/grid-forming hybrid mode control technologies is prospected. © 2024 Automation of Electric Power Systems Press. All rights reserved.