High-altitude electromagnetic pulse (HEMP), as a wide-area electromagnetic attack method, can have severe impacts on the power equipment and even collapse the power infrastructure, posing significant challenges to the electromagnetic safety of novel power systems. This article focuses on the latest research progress on the power system effects in late-time HEMP environment. Firstly, the mechanism of geomagnetic disturbance generation and the calculation method of induced geomagnetic field are analyzed. The calculation method of geomagnetically induced current (GIC) is provided. Then, the effects and mechanisms of typical primary power equipment, such as power transformers, current transformers, circuit breakers, etc. under extreme GIC conditions are summarized. Next, the extreme GIC injection devices and simulated experiment methods are discussed. And the experimental and simulation results acquired by Defense Threat Reduction Agency (DTRA) and Electric Power Research Institute (EPRI) are also discussed, as well as the power system effects simulation and assessment. Finally, the article summarises the present work, and analyzes the future research from the perspective of effects mechanism, primary power equipment characteristics, simulated experimental methods, and system-level effects assessment.