In this talk we introduce the concept of elastic networks, which are network models with mechanical interactions, and discuss how these network models have been widely used in soft matter physics and materials science to understand interesting phenomena of mechanics. We will then focus on elastic networks that exhibit topological edge floppy modes, which belong to the new field of "topological mechanics". We will discuss our recent work on applying ideas from topological mechanics to design novel mechanical metamaterials with exotic properties, such as being able to switch from hard to soft, and switch back again. Speaker(s): Xiaoming Mao (University of Michigan, Physics)