Land subsidence is probably one of the most evident environmental effects of groundwater pumping. Globally, freshwater demand is the leading cause of this phenomenon. Land subsidence induced by aquifer system drainage can reach total values of up to 14.5 m. The spatial extension of this phenomenon is usually extensive and is often difficult to define clearly. Aquifer compaction contributes to many socio-economic effects and high infrastructure-related damage costs. Currently, many methods are used to analyze aquifer compaction. These include the fundamental relationship between groundwater head and groundwater flow direction, water pressure and aquifer matrix compressibility. Such solutions enable satisfactory modelling results. However, further research is needed to allow more efficient modelling of aquifer compaction. Recently, satellite radar interferometry (InSAR) has contributed to significant progress in monitoring and determining the spatio-temporal land subsidence distributions worldwide. Therefore, implementation of this approach can pave the way to the development of more efficient aquifer compaction models. This paper presents (1) a comprehensive review of models used to predict land surface displacements caused by aquifer drainage, as well as (2) recent advances, and (3) a summary of InSAR implementation in recent years to support the aquifer compaction modelling process.