Multi-robot path planning, aimed at finding conflict-free paths for multiple robots to navigate from their initial positions to their respective target positions within a shared working environment, is pivotal in multi-robot collaborative planning. However, practical factors such as clock drift, moving obstacles and machine faults may lead to temporal deviations between actual and planned execution processes of the multi-robot system, resulting in unexpected conflicts among robots. Robust multi-robot path planning under uncertainty, along with ensuring the safe execution of plans to a certain extent, is a research hotspot in the field of path planning. This article begins by summarizing the problem description of multi-robot path planning under uncertainty. It then reviews existing studies from perspectives of robust planning algorithms and online execution strategies as well as corresponding evaluation metrics. The logic and characteristics of various methods are discussed. Finally, the future research directions of the critical technologies in robust multi-robot path planning are put forward.