Liquid crystal polymers (LCPs) are functional polymers that have both the orientational order of liquid crystal and mechanical properties of polymers. The introduction of structural units with photochemical isomerization or photothermal response into liquid crystal polymers can make them undergo phase transition under light or thermal stimulation, inducing macroscopic deformation. After LCPs are oriented by one-step or two-step alignment methods, the alignment of the LCPs can be programmed. Shape changing of LCPs has potential applications in the fields of biomimetic soft robots, microfluidics, soft actuators, structural color and anti-counterfeiting. This review introduces the major orientation techniques for liquid crystal polymers and developed shape-change-based functions, and finally, an outlook of LCPs in future technological applications is proposed.