The advances in micro- and nanofabrication technologies enable the preparation of increasingly smaller mechanical transducers capable of detecting the forces, motion, mechanical properties and masses that emerge in biomolecular interactions and fundamental biological processes. Thus, biosensors based on nanomechanical systems have gained considerable relevance in the last decade. This review provides insight into the mechanical phenomena that occur in suspended mechanical structures when either biological adsorption or interactions take place on their surface. This review guides the reader through the parameters that change as a consequence of biomolecular adsorption: mass, surface stress, effective Young's modulus and viscoelasticity. The mathematical background needed to correctly interpret the output signals from nanomechanical biosensors is also outlined here. Other practical issues reviewed are the immobilization of biomolecular receptors on the surface of nanomechanical systems and methods to attain that in large arrays of sensors. We then describe some relevant realizations of biosensor devices based on nanomechanical systems that harness some of the mechanical effects cited above. We finally discuss the intrinsic detection limits of the devices and the limitation that arises from non-specific adsorption.