Complex surfaces typically including aspheres are more and more widely used in modern optical systems. Better imaging quality can be achieved with fewer elements because aspheres provide more design freedom. However, the variety of aspheres also introduces challenges to surface metrology. Conventional null tests do not have the flexibility to adapt to different shapes. Therefore variable aberration compensation techniques are important to enhance the flexibility and efficiency of testing. The analysis of partial null lens, combination of phase plates and high-order aspheric singlet for variable compensation schemes of spherical aberration of rotationally symmetric aspheres is presented. For aberration compensation of off-axis aspheres, the variable compensation schemes of tilted spherical mirror system, Risley prisms and the counter-rotating phase plates are analyzed. Furthermore, the progress of using deformable mirrors and spatial light modulators (SLM) as programmable compensators in wavefront interferometry is reviewed. Finally, three major problems in variable aberration compensation techniques are introduced, which are compensation of wide range and multiple modes of aberration, retrace error compensation and decoupling of misalignment-induced aberration.