Unlike slip bonds, catch bonds experience reinforcement under tension. Cell adheres to the surface, using integrins forming both catch- and slip- bonds with the surface receptors. How will the catch and slip bonds interact with each other on a single adhesion scale? How does the intracellular structure vary depending on the extracellular matrix stiffness? I discuss the implications of single catch-bond characteristics for the behavior of a load-sharing cluster of such bonds: these are shown to possess a regime of strengthening with increasing applied force, similar to the manner in which focal adhesions become selectively reinforced. In addition, I present numerical simulations of mixtures of catch and slip bonds within single focal adhesion, and propose a model of how they can influence cytoskeletal reorganization, force generation and adhesion growth, interacting indirectly through applied force. Our results may shed new light on the fundamental processes that allow cells to sense the mechanical properties of their environment and in particular show how single focal adhesions may act, autonomously, as local rigidity sensors.