Hydrogels are three-dimensional crosslinked structures with physicochemical properties similar to the extracellular matrix (ECM). By changing the hydrogel’s material type, crosslinking, molecular weight, chemical surface, and functionalization, it is possible to mimic the mechanical properties of native tissues. Hydrogels are currently used in the biomedical and pharmaceutical fields for drug delivery systems, wound dressings, tissue engineering, and contact lenses. Lately, research has been focused on hydrogels from natural sources. Polysaccharides have drawn attention in recent years as a promising material for biological applications, due to their biocompatibility, biodegradability, non-toxicity, and excellent mechanical properties. Polysaccharide-based hydrogels can be used as drug delivery systems for the efficient release of various types of cancer therapeutics, enhancing the therapeutic efficacy and minimizing potential side effects. This review summarizes hydrogels’ classification, properties, and synthesis methods. Furthermore, it also covers several important natural polysaccharides (chitosan, alginate, hyaluronic acid, cellulose, and carrageenan) widely used as hydrogels for drug delivery and, in particular, their application in cancer treatment.