Abstract Carbohydrate polymers are ubiquitous in biological systems and their roles are highly diverse, ranging from energy storage over mechanical stabilisation to mediating cell-cell or cell-protein interactions. The functional diversity is mirrored by a chemical diversity that results from the high flexibility of how different sugar monomers can be arranged into linear, branched or cyclic polymeric structures. Mathematical models describing biochemical processes on polymers are faced with various difficulties. First, polymer-active enzymes are often specific to some local configuration within the polymer but are indifferent to other features. That is they are potentially active on a large variety of different chemical compounds, meaning that polymers of different size and structure simultaneously compete for enzymes. Second, especially large polymers interact with each other and form water-insoluble phases that restrict or exclude the formation of enzyme-substrate complexes. This heterogeneity of the reaction system has to be taken into account by explicitly considering processes at the, often complex, surface of the polymer matrix. We review recent approaches to theoretically describe polymer biochemical systems. All attempts address a particular challenge, which we discuss in more detail. We emphasise a recent attempt which draws novel analogies between polymer biochemistry and statistical thermodynamics and illustrate how this parallel leads to novel insights about non-uniform polymer reactant mixtures. Finally, we discuss the future challenges of the young and growing field of theoretical polymer biochemistry.