In conventional compression treatment using bandage or stocking, always there has been a problem of achieving and maintaining the recommended compression gradient and level. In addition, these devices are incapable of offering dynamic (massaging) compression, often preferred especially for senior and non-active patients to improve blood flow. To overcome these challenges, the application of shape memory materials is proven to provide a dynamic or selective pressure change directly on the limb. Memory material-based stockings or bandage have the potential to tackle the drawbacks of existing stockings by allowing users to modify pressure levels externally as needed during compression therapy, i.e. as a smart wound care device. This paper reports the consolidated information on traditional compression systems, their challenges, and modern methods involving active compression bandages based on smart materials technology (via shape memory polymer or shape memory alloy), which develop intermittent active pressure to alleviate the symptoms of lower limb problems.