Micro and nanomechanical systems are being adopted in billions of products, that address a wide range of sensor and actuator applications in modern technology. The advent of two-dimensional materials, and the ability to fabricate atomically thin membranes like graphene, promises further device downscaling, enabling ultimate sensing capabilities that until recently were only dreamed of. However, owing to their small size, these membranes exhibit nonlinearities at nm amplitudes and obtain a wealth of nonlinear phenomena whose potential in sensing applications are to be explored.