The millimeter wave (mmW) band, commonly referred to as the frequency band between 30 GHz and 300 GHz, is seen as a possible candidate to increase achievable rates for mobile applications due to the existence of free spectrum. However, the high path loss necessitates the use of highly directional antennas. Furthermore, impairments and power constraints make it difficult to provide full digital beamforming systems. In this thesis, we approach this problem by proposing effective beam alignment and beam tracking algorithms for low-complex analog beamforming (ABF) systems, showing their applicability by experimental demonstration. After taking a closer look at particular features of the mmW channel properties and introducing the beamforming as a spatial filter, we begin our investigations with the application of detection theory for the non-convex beam alignment problem. Based on an M-ary hypothesis test, we derive algorithms for defining the length of the training signal efficiently. Using the concept of black-box optimization algorithms, which allow optimization of non-convex algorithms, we propose a beam alignment algorithm for codebook-based ABF based systems, which is shown to reduce the training overhead significantly. As a low-complex alternative, we propose a two-staged gradient-based beam alignment algorithm that uses convex optimization strategies after finding a subregion of the beam alignment function in which the function can be regarded convex. This algorithm is implemented in a real-time prototype system and shows its superiority over the exhaustive search approach in simulations and experiments. Finally, we propose a beam tracking algorithm for supporting mobility. Experiments and comparisons with a ray-tracing channel model show that it can be used efficiently in line of sight (LoS) and non line of sight (NLoS) scenarios for walking-speed movements.