Platelets are involved in life-sustaining processes such as hemostasis, wound healing, atherothrombosis and angiogenesis. Mechanical trauma to blood vessels causes platelet activation resulting in their adherence and clot formation at the damaged site, culminating in clot retraction and tissue repair. Two of the major players underlying this process are the cytoskeleton, i.e., actin and microtubules, and the membrane integrin receptors. Rare congenital bleeding disorders such as Glanzmann thrombasthenia and Bernard-Soulier syndrome are associated with genetic alterations of platelet surface receptors, also affecting the platelet cytoskeletal structure. In this review, we summarize the current knowledge about platelet structure and adhesion, and delve into the mechanical aspects of platelet function. Platelets lack a nucleus, and can thus provide a minimal model of a biological cell. New biophysical tools may help to scrutinize platelets anew and to extend the existing knowledge on cell biology.