Network theory has led to the abstraction of many real-world systems and enabled their modelling as simple networks comprising nodes and edges. In particular, in the field of biological sciences, network theory provides a robust framework to capture the complexity inherent to biological systems. Networks in biology have been modelled at different scales, starting from cells to population levels. These models have provided crucial insights into the evolution, mechanism, and functions of several biological systems. However, most natural and engineered systems are composed of multiple subsystems and layers of connectivity. A multilayer network paradigm has proven useful in understanding such systems. Here, we have briefly introduced the network formalism of modelling biological systems at various levels. This is followed by an introduction to multilayer networks. Multilayer networks have been utilized to model biological systems at multiple scales ranging from protein-protein interactions, transcription and metabolic networks, to ecological networks involving interactions between species. Recent advances in studying the structure and dynamics of such multilayer networks have enabled a better understanding of the complexity in these biological systems. Finally, we discuss the recent advances in studying the structure and dynamics of such multilayered networks followed by the challenges and future prospects.