One-dimensional measurement along the Line-Of-Sight (LOS) direction has greatly limited the capability of InSAR technique in the investigation of surface displacements and their dynamics. In recent years, great efforts have been made to resolve complete three-dimensional (3-D) displacements from InSAR measurements. This contribution is intended to provide a systematic review of the progress achieved in this field. Based on an analysis of the InSAR LOS measurements, we first cover two commonly used techniques, i.e., Offset-Tracking and multi-aperture InSAR (MAI), with which the surface displacement in the azimuth direction can be measured together with the LOS displacement. Several methods for mapping 3-D displacements using InSAR measurements are subsequently presented and categorized into three groups: (i) combination of multi-pass LOS and azimuth measurements; (ii) integration of InSAR and GPS data; and (iii) prior information assisted approaches. The strengths and weaknesses of each method are analyzed to show the applicability of each method to specific 3-D displacement mapping cases, in hope to provide a useful guidance in choosing a suitable approach accordingly. Finally, suggestions for resolving the challenging issues and outlook of future research are given.