Rapid recent progress in advanced microscopy has revealed that nano-particles immersed in biological uids exhibit rich and widely varied behaviors. In some cases, biology serves to enhance the mobility of small scale entities. Cargo-laden vesicles in axons undergo stark periods of forward and backward motion, inter- rupted by sudden pauses and periods of free diusion. Over large periods of time, the motion is eectively that of a particle with steady drift accompanied a diu- sive spread greater than what can be explained by thermal uctuations alone. As another example, E. coli and other bacteria are known to respond to the local con- centration of nutrients in such a way that they can climb gradients toward optimal locations. Again, the eective behavior is drift toward a desired" location, with enhanced diusivity. In other cases, biological entities are signicantly slowed. Relatively large parti- cles diusing in uids such as mucus, blood, biolms or the cytoplasm of cells all experience hinderances due to interactions with the polymer networks that consti- tute small-scale biological environments. Researches repeatedly observe sublinear growth of the mean-squared displacement of particle paths. This signals to theo- reticians that the particles are not experiencing traditional Brownian motion. In- terestingly, many viruses are actually small enough to avoid this type of hinderance when moving through human mucus. However, the body's immune response in- cludes teams of still smaller antibodies that can immobilize virions by serving as an intermediary creating binding events between virions and the local mucin network. Underlying the mathematical description of all these phenomena is a modeling framework that employs stochastic dierential equations, hybrid switching diu- sions and stochastic integro-dierential equations. We will begin with the Langevin model for diusion. This is the physicist's view of Brownian motion, derived from Newton's Second Law. We will see how the traditional mathematical view of Brow- nian motion arises by taking a certain limit. The force-balance view permits a variety of generalizations that include particle-particle interactions, the in uence of external energy potentials, and viscoelastic force-memory eects. We will use sto- chastic calculus to derive important statistics for the paths of such particles, develop simulation techniques, and encounter a number of unsolved theoretical problems.