Vapor compression refrigeration is one of the more promising alternatives to conventional electronics cooling techniques, especially at high ambient temperature. For the use of refrigeration in electronics cooling, a miniature-scale, low cost, and reliable refrigerant compressor is needed. An electrostatically actuated diaphragm compressor is a promising concept for this application. The compressor consists of a flexible circular diaphragm clamped at its circumference inside a conformal chamber. The membrane and the chamber surfaces are coated with metallic electrodes. A potential difference applied between the diaphragm and the chamber pulls the diaphragm towards the chamber surface progressively from the outer circumference towards the center. This zipping actuation reduces the volume available to the refrigerant gas, thereby increasing its pressure. A segmentation technique is proposed for analysis of the compressor by which the domain is divided into multiple segments for each of which the forces acting on the diaphragm are estimated. The pull-down voltage to completely zip each individual segment is thus obtained. The required voltage for obtaining a specific pressure rise in the chamber can thus be determined. Predictions from the model compare well with other simulation results from the literature, as well as to experimental measurements of the diaphragm displacement and chamber pressure rise in a custom-built setup. A dynamic compressor model is also developed in which the dynamic forces induced due to the finite-time deflection of the diaphragm are taken into consideration using the segmentation approach developed in the quasi-static model. Results from the analytical model compare favorably with those from a detailed numerical simulation as well as with experimental measurements available in the literature. A finite element quasi-static model is also developed for further validation of the analytical model. Based on the simulation model predictions, the design of the diaphragm compressor is optimized for the maximum performance. Since the desired cooling performance is not possible with a single compressor unit, a 3-D array for boosting the pressure rise and the volume flow rate is proposed. Finally, suggested future work on diaphragm compressors is outlined