Through the perspective of the current glycomics age, fucanomics and galactanomics denote the international projects concerned with the studies of the biomedically active marine sulfated fucose- or galactose-composed polysaccharides, named sulfated fucans (SFs), and sulfated galactans(SGs), respectively. SFs and SGs are isolated from algae or marine invertebrates. The range of therapeutic actions of SFs and SGs is impressively broad. When certain structural requirements are found, some SFs and SGs may exhibit beneficial properties in inflammation, nociception, hemostasis (coagulation and thrombosis), vascular biology (angiogenesis), oncology, oxidative-stress, and virus infections. Although many biomedical applications for SFs and SGs have been pointed out over the past two decades, only inflammation, hemostasis, cancer, and vascular biology have their mechanisms of action satisfactorily elucidated. In addition, advanced structure-function relationships have been achieved only for the anticoagulant and antithrombotic activities, in which glycans of well-defined structures have been assayed. Because of this, the activities of SFs and SGs in stopping the clot and thrombus formation represent the closest therapeutic areas of having these glycans truly explored for drug development. Here, through an analytical viewpoint, we present the common methods and protocols employed to achieve such advanced structure-function relationships of SFs and SGs in anticoagulation and antithrombosis.