Blood coagulation and fibrinolysis systems are enzymatic cascades in blood plasma that control formation and dissolution of a fibrin clot, respectively. However, critical processes in both systems occur on specialized scaffolds but not in the liquid phase. These scaffolds are two- or three-dimensional matrices that provide special conditions for biochemical reactions. The following fundamental categories of scaffolds can be distinguished: (a) phospholipid membranes enriched with phosphatidylserine provided by a procoagulant subpopulation of activated platelets, as well as damaged endothelium; membranes of apoptotic bodies in atherosclerotic plaque; lipoproteins and plasma microvesicles; (b) complex of fibrin and extracellular matrix proteins, which is associated with platelets and is the leading scaffold for pro- and anti-fibrinolytic processes; (c) polymers containing phosphate groups, including platelet polyphosphates and neutrophil extracellular traps. For some of these scaffolds, there are speculations about their physiological significance and physical meaning, while the role of others seems mysterious or at least pathophysiological. Herein we consider existing ideas about the roles and mechanisms of the involvement of these scaffolds in haemostasis and thrombosis.