Fucoidan or fucoidans cover a family of sulfated fucose-rich polysaccharides, built of a backbone of L-fucose units, and characteristically found in brown seaweeds. Fucoidans have potential therapeutic properties, including anti-inflammatory and anti-coagulant activities, as well as anti-proliferative effects on cancer cells. Recent work has revealed distinct structural features of fucoidans obtained from different brown seaweed sources. Fucoidans are classically obtained from brown seaweeds by multi-step, hot acid extraction, but the structural and compositional traits, and possibly the bioactivity, of the fucoidan polysaccharides are significantly influenced by the extraction parameters. This review discusses the structural features of fucoidans, the significance of different extraction technologies, and reviews enzymatic degradation of fucoidans and the use of fucoidan-modifying enzymes for elucidating structural details of fucoidans. Mild extraction techniques coupled with the use of new tools such as enzymes can provide the much needed knowledge about structural characteristics of different fucoidan molecules and thus pave the way for a better understanding of the structural chemistry and bioactivities of fucoidans.