Marine sulfated polysaccharides (MSP), such as sulfated fucans (SF), sulfated galactans (SG) and glycosaminoglycans (GAG) isolated from either algae or invertebrate animals, are highly anionic polysaccharides capable of interacting with certain cationic proteins, such as (co)-factors of the coagulation cascade during clotting-inhibition processes. These molecular complexes between MSP and coagulation-related proteins might, at first glance, be assumed to be driven mostly by electrostatic interactions. However, a systematic comparison using several novel sulfated polysaccharides composed of repetitive oligosaccharides with clear sulfation patterns has shown that these molecular interactions are regulated essentially by the stereochemistry of the glycans (which depends on a conjunction of anomericity, monosaccharide, conformational preference, and glycosylation and sulfation sites), rather than just a simple consequence of their negative charge density (mainly the number of sulfate groups). Here, we present an overview of the structure-function relationships of MSP, correlating their structures with their potential anticoagulant and antithrombotic actions, since pathologies related to the cardiovascular system are one of the major causes of illness and mortality in the world.