The design of beam position monitors often involves challenging system design choices. Position transducers must be robust, accurate, and generate adequate position signal without unduly disturbing the beam. Electronics must be reliable and affordable, usually while meeting tough requirements on precision, accuracy, and dynamic range. These requirements may be difficult to achieve simultaneously, leading the designer into interesting opportunities for optimization or compromise. Some useful techniques and tools are shown. Both finite element analysis and analytic techniques will be used to investigate quasi-static aspects of electromagnetic fields such as the impedance of and the coupling of beam to striplines or buttons. Finite-element tools will be used to understand dynamic aspects of the electromagnetic fields of beams, such as wake fields and transmission-line and cavity effects in vacuum-to-air feedthroughs. Mathematical modeling of electrical signals through a processing chain will be demonstrated, in particular to illuminate areas where neither a pure time-domain nor a pure frequency-domain analysis is obviously advantageous. Emphasis will be on calculational techniques, in particular on using both lime domain and frequency domain approaches to the applicable parts of interesting problems.