Summary: The topic of estimating motion is a major issue for a wide range of applications. We study techniques for tracking given different external requirements. We start by studying models for direct tracking where estimating motion is possible without preprocessing. We extend established optical flow models in order to improve their performance in connection with complex motion. We analyze these models and check their performance based on different synthetic and real data sets. As a specific example we study microscopy data of migrating cells and illustrate the required mathematical tasks. For the second theoretical part we consider types of data that require reconstruction in order to obtain images that are needed to estimate motion. We present a model for simultaneous reconstruction and motion estimation. We apply this model to dynamic X-ray tomography data. We consider moving objects measured from only one or two different angles per time step.