High-capacity anodes, such as Si, have attracted tremendous research interests from the last two decades because of the requirement for high energy density of next-generation lithium-ion batteries (LIBs). The mechanical integrity and stability of such materials during cycling are critical because their volume considerably changes. The volume changes/deformation result in mechanical stresses, which lead to mechanical failures, including cracks, fragmentation, and debonding. These phenomena accelerate capacity fading during electrochemical cycling and thus limit the application of high-capacity anodes. Experimental studies have been performed to characterize the deformation and failure behavior of these high-capacity materials directly, providing fundamental insights into the degradation processes. Modeling works have focused on elucidating the underlying mechanisms and providing design tools for next-generation battery design. This review presents an overview of the fundamental understanding and theoretical analysis of the electrochemical degradation and safety issues of LIBs where mechanics dominates. We first introduce the stress generation and failure behavior of high-capacity anodes from the experimental and computational aspects, respectively. Then, we summarize and discuss the strategies of stress mitigation and failure suppression. Finally, we conclude the significant points and outlook critical bottlenecks in further developing and spreading high-capacity materials of LIBs.