Cell motility and migration are central to the development and maintenance of multicellular organisms, and errors during this process can lead to major diseases. Consequently, the mechanisms and phenomenology of cell motility are currently under intense study. In recent years, a new interdisciplinary field focusing on the study of biological processes at the nanoscale level, with a range of technological applications in medicine and biological research, has emerged. The work presented in this thesis is at the interface of cell biology, image processing, and stochastic modeling. The stochastic models introduced here are based on persistent random motion, which I apply to real-life studies of cell motility on flat and nanostructured surfaces. These models aim to predict the time-dependent position of cell centroids in a stochastic manner, and conversely determine directly from experimental recordings of cell motility the various motility parameters. This can aid the experimentalist to draw biologically relevant conclusions about cell-substrate interactions. The need to track cells in a large number of movies has raised the question of automation of cell tracking and that of reproducibility and robustness of cell centroid measurement. To address this, I wrote the PACT cell tracking program, which is optimized for uniform as well as non-uniform backgrounds such as nanostructured surfaces. Rapid progress in the field of the automation of cell tracking steered us into a comparative study of PACT’s performance against other cell tracking programs. We find that different programs yield somewhat different results when applied to the same movie of migrating cells but that the differences are not statistically significant. To introduce persistent random motion, I first present a study of idealized random motion in two dimensions. This finds direct application to experimental studies of cell membrane fluidity and membrane protein dynamics, and I improve on the methodology currently used in that field by showing how to assess the randomness of the motility and how to optimally determine the diffusion coefficient. By adding a persistence component to simple random motion I introduce the standard Ornstein-Uhlenbeck process. I build on this commonly used cell motility model to address the challenges of working with real-life data: positional (centroid coordinate measuring) error and time discretization (due to finite frame rate in a movie of motile cells). This includes optimally measuring the motility parameters and balancing precision of measurement against the mathematical complexity of real-life models of cell motility. Finally, I expanded our understanding of cell response to surface topography by generalizing the Orstein-Uhlenbeck process to study cell motility on anisotropic substrates. I apply the general model to analyze cell motility on a series of anisotropic substrates and discuss the implications of our observations. This work is potentially useful to cell biologists by addressing their need for precise yet simple tools for studies of cell motility. The advances in the theoretical understanding of motility presented here bear the experimentalists’ needs in mind, and can find direct technological applications such as cell guidance and growth using nanotopography.