Recent advances in nanotechnology have led to the development of nano-electro-mechanical systems (NEMS) such as nanomechanical resonators, which have recently received significant attention from the scientific community. This has not only been for their capability for the label-free detection of bio/chemical-molecules at single-molecule (or atomic) resolution for future applications such as the early diagnostics of diseases such as cancer, but also for their unprecedented ability to detect physical quantities such as molecular weight, elastic stiffness, surface stress, and surface elastic stiffness for adsorbed molecules on the surface. Most experimental works on resonator-based molecular detection have been based on the principle that molecular adsorption onto a resonator surface increases the effective mass, and consequently decreases the resonant frequencies of the nanomechanical resonator. However, this principle is insufficient to provide fundamental insights into resonator-based molecular detection at the nanoscale; this is due to recently proposed novel nanoscale detection principles including various effects such as surface effects, nonlinear oscillations, coupled resonance, and stiffness effects. Furthermore, these effects have only recently been incorporated into existing physical models for resonators, and therefore the universal physical principles governing nanoresonator-based detection have not been completely described. Therefore, our objective in this review is to overview the current attempts to understand the underlying mechanisms in nanoresonator-based detection using physical models coupled to computational simulations and/or experiments. Specifically, we will focus on issues of special relevance to the dynamic behavior of nanoresonators and their applications in biological/chemical detection: the resonance behavior of micro/nano-resonators; resonator-based chemical/biological detection; physical models of various nanoresonators such as nanowires, carbon nanotubes, and graphene. We pay particular attention to experimental and computational approaches that have been useful in elucidating the mechanisms underlying the dynamic behavior of resonators across multiple and disparate spatial/length scales, and the resulting insight into resonator-based detection that has been obtained. We additionally provide extensive discussion regarding potentially fruitful future research directions coupling experiments and simulations in order to develop a fundamental understanding of the basic physical principles that govern NEMS and NEMS-based sensing and detection applications.