Identifying new drug candidates remains a critical and complex challenge in drug development. Recent advances in deep learning have demonstrated significant potential to accelerate this process, particularly through the use of protein language models (pLMs). These models aim to effectively capture the structural and functional properties of proteins by embedding them in high-dimensional spaces, thereby providing powerful tools for predictive tasks. This review examines the application of pLMs in drug-target interaction (DTI) prediction, addressing both small-molecule and protein-based therapeutics. We explore diverse methodologies, including end-to-end learning models and those that leverage pre-trained foundational pLMs. Furthermore, we highlight the role of heterogeneous data integration-ranging from protein structures to knowledge graphs-to improve the accuracy of DTI predictions. Despite notable progress, challenges persist in accurately identifying DTIs, mainly due to data-related limitations and algorithmic constraints. Future research directions include utilising multimodal learning approaches, incorporating temporal/dynamic interaction data into training, and employing novel deep learning architectures to refine protein representations, gain a deeper understanding of biological context regarding molecular interactions, and, thus, advance the DTI prediction field.