Elastic compression of the lower leg is the traditional preventive and curative treatment of venous insufficiency. After presenting the medical strategies related to compression therapies, this chapter develops current advances in clinics as well as in engineering and outline the more important knowledge arising from this review. Compression hosiery acts by providing pressure to the leg. Pressure generation using socks mainly depends on the stiffness and the size of the socks, the size of the leg, but also the leg morphology. In the case of bandages, the role of friction must be outlined, as the main factor in maintaining the bandage wrapped around the leg, but also as an influencing factor in pressure generation. Besides generated pressure, response of superficial veins to compression also depends on the vein size and the fat stiffness. But mechanical assessments should not mask the importance of other factors such as muscular contraction or nurse formation. An important impact of these results would be head towards an improved personalization of compression treatment.