Glycosaminoglycans (GAGs) represent a formidable frontier for chemists, biochemists, biologists, medicinal chemists and drug delivery specialists because of massive structural complexity. GAGs are arguably the most complex, natural linear biopolymers with theoretical diversity orders of magnitude higher than proteins and nucleic acids. Yet, this diversity remains generally untapped. Computational approaches offer major routes to understand GAG structure and dynamics so as to enable novel applications of these biopolymers. In fact, computational algorithms, softwares, online tools and techniques have reached a level of sophistication that help understand atomistic details of conformational variation and protein recognition of individual GAG sequences. This review describes current approaches and challenges in computational study of GAGs. It presents a history of major findings since the earliest mention of GAGs (the 1960s), the development of parameters and force fields specific for GAGs, and the application of these tools in understanding GAG structure-function relationship. This review also presents a section on how to perform simulation of GAGs, which is directed toward researchers interested in entering this promising field with potential to impact therapy.