In recent years, wearable electronic devices have developed rapidly and flexible sensors have been increasingly used in medical, aerospace, automotive, industrial and commercial applications. Flexible pressure sensors are critical in human-robot interaction, physiological signal monitoring and robotic haptics. Among them, capacitive type flexible pressure sensors are widely used due to their unsophisticated structure, good stability, small temperature deviation and environmentally friendly. Currently, most of capacitive sensors adopt the design with an electrical membrane inserted between two electrodes. This paper presents a comprehensive review of the development of flexible capacitive pressure sensor from the perspective of technological and engineering developments. This paper firstly introduces the capacitive pressure sensor by using the working mechanism as an entry point. Secondly, this paper discusses three general methods to increase the sensitivity of pressure sensing, including changing the dielectric microstructure, the dielectric constant, and different dielectric materials. Finally, the advantages and disadvantages of three methods for sensitivity improvement were discussed.