Critical mechanical structures are structures at the verge of mechanical instability. They play important roles in modeling how soft matter systems resist or flow under stress.  At the same time, critical mechanical structures are also excellent candidates for the design of mechanical metamaterials, due to both their convenient reconfigurability and topologically protected excitations at boundaries and interfaces of these structures, known as topological zero modes and states of self stress.  In this talk, we discuss fundamental concepts in topological mechanics of critical mechanical structures and review recent theoretical and experimental advances on their applications in mechanical metamaterials.