Advances in nanotechnology are yielding exciting opportunities for the study of biological systems and the development of biomedical applications. Examples range from the sorting of cells using nanoparticles down to the manipulation of a single biomolecule within a nanofluidic device. Computer simulations offer key insight into the mechanisms underlying these applications. In this talk, I will discuss two systems that lie at the intersection of nanotechnology and biophysics. To begin, I will focus on the translocation of a polymer across a membrane, in particular sequencing DNA using a nanopore. Results from computer simulations examining translocation in a "crowded environment" where there are obstacles on both sides of the membrane will be presented. During the second portion of the talk, I will discuss the use of clusters of superparamagnetic iron-oxide nanoparticles as contrast agents in MRI. In addition to an overview of the dynamics of this process, I will present results from simulation and experimental work studying the effects of encapsulating the particles with a hydrophilic polymer coating.