The marine reservoir, with its massive biodiversity, likely harbors numerous human drug candidates. Polysaccharides of various marine origins have shown to be good alternatives to mammalian polysaccharides. One well-known example is heparin, a sulfated polysaccharide used in the prevention of thrombosis and pulmonary embolism. The oldest use of marine polysaccharides concerns those produced by algae. These products form the basis for an economically important and expanding global industry. This chapter provides a historical background to the discovery of the therapeutic potential of these marine compounds, together with their medical and biotechnological applications. Peripheral arterial disease (PAD) is a progressive disorder due to atherosclerosis (narrowing of the peripheral arteries, especially in the legs). Arterial flow is reduced or discontinuous, causing oxygen deprivation in the underlying tissues and possible tissue necrosis. The primary aim of medical therapy is to increase arterial flow in the affected limb in order to relieve pain, heal trophic lesions, and avoid amputation. Anticoagulant, antithrombotic, and antiplatelet agents are used to reduce the risk of thrombus formation. Novel treatments such as therapeutic angiogenesis (promotion of new blood vessel growth) are in the development phase, with promising preclinical data. Fucoidan is a polysulfated l-fucose endowed with biological activities closely related to its chemical composition (especially the distribution of sulfate groups along its polyfucose backbone) and to its molecular weight. Fucoidans are highly soluble in water, nontoxic, and non-immunogenic. Details are provided below on its production and characterization and on the main chemical characteristics that influence their biological activities. Fucoidan exhibits venous and arterial antithrombotic properties in animal models. In animal experiments, fucoidan promoted the formation of new blood vessels, thereby preventing necrosis of ischemic tissue. It also recruits stem cells from bone marrow, further accelerating tissue healing. The cellular and molecular mechanisms underlying fucoidan's effects on angiogenesis are then addressed, beginning with a brief overview of blood vessel formation. Recent advances have been made in understanding how the interactions between these polyfucoses and adult stem cells contribute to new blood vessel formation after ischemic injury, notably via carbohydrates located mainly in the basement membrane and cell surface.