Carbon nanotube and graphenemechanical resonators constitute the ultimate size limit for one- and two-dimensional nano-electromechanical systems (NEMS). Their low dimensionality translates into strikingly unusual mechanical properties. Firstly, graphene and nanotube NEMS are so light that they can respond to variations of mass at the subatomic level [1]. Secondly, the dynamics of these NEMS features strong dissipative nonlinearities, even in the limit of very weak driving forces. This means that the damping forcedepends on the motional amplitude, as a result of which the mechanical quality factor increases to high values as the amplitude of the driving force is decreased [2].Combining low mass and high quality factor enables highly sensitive force detection. Our group has shown that force detectors based on nanotube NEMS have an unprecedented sensitivity on the scale of 10 zepto Newton per square root of Hertz (1zN=1E-21N) at a temperature of 1.2 K [3]. This makes it possible to measure the Brownian vibrations of the nanotube down to cryogenic temperatures.In this talk, I will first introduce our work on graphene and nanotube NEMS, and will briefly discuss their nonlinear dynamics. I will then present our work on zepto Newton force detection. I will show how Brownian vibrations interact with other mechanical modes, and how they couple to single electron tunneling events in the Coulomb blockade regime. Finally, I will propose that force sensing with nanotube resonators may offer new opportunities for detecting and manipulating individual nuclear spins.