Binding sites are key components of biomolecular structures, such as proteins and RNAs, serving as hubs for interactions with other molecules. Identification of the binding sites in macromolecules is essential for structure-based molecular and drug design. However, experimental methods for binding site identification are resource-intensive and time-consuming. In contrast, computational methods enable large-scale binding site identification, structure flexibility analysis, as well as assessment of intermolecular interactions within the binding sites. In this review, we describe recent advances in binding site identification using machine learning methods; we classify the approaches based on the encoding of the macromolecule information about its sequence, structure, template knowledge, geometry, and energetic characteristics. Importantly, we categorize the methods based on the type of the interacting molecule, namely, small molecules, peptides, and ions. Finally, we describe perspectives, limitations, and challenges of the state-of-the-art methods with an emphasis on deep learning-based approaches. These computational approaches aim to advance drug discovery by expanding the druggable genome through the identification of novel binding sites in pharmacological targets and facilitating structure-based hit identification and lead optimization.