Helicobacter pylori possesses a broad spectrum of pathogenic factors that allow it to survive and colonize the gastric mucosa, and thus, the pathogenetic targets, which have the same diversity, require search for and the development of alternative, effective, and innocuous means for the eradication of H. pylori. In recent years, fucoidans have been extensively studied due to the numerous interesting biological activities, including the anti-adhesive, anti-oxidative, antitoxic, immunomodulatory, anticoagulant, and anti-infection effects. This review summarizes the data on the effects of extracts and sulfated polysaccharides of marine algae, mainly fucoidans, on pathogenic targets in Helicobacter infection. The pathogenetic targets for therapeutic agents after H. pylori infection, such as flagellas, urease, and other enzymes, including adhesins, cytotoxin A (VacA), phospholipase, and L-8, are characterized here. The main target for the sulfated polysaccharides of seaweed is cell receptors of the gastric mucosa. This review presents the published data about the pleiotropic anti-inflammatory effects of polysaccharides on the gastric mucosa. It is known that fucoidan and other sulfated polysaccharides from algae have anti-ulcer effects, prevent the adhesion of H. pylori to, and reduce the formation of biofilm. The authors speculate that the effect of sulfated polysaccharides on the infectious process caused by H. pylori is related to their action on innate and adaptive immunity cells, and also anti-oxidant and antitoxic potential. Presented in the review are materials indicated for the study of extracts and sulfated polysaccharides from seaweed during H. pylori infection, as these compounds are characterized by multimodality actions. Based on the analysis of literary materials in recent years, the authors concluded that fucoidan can be attributed to the generation of new candidates to create drugs intended for the inclusion in the scheme of eradication therapy of H. pylori infection.