Drug discovery requires a tremendous amount of time and cost. Computational drug-target interaction prediction, a significant part of this process, can reduce these requirements by narrowing the search space for wet lab experiments. In this survey, we provide comprehensive details of graph machine learning-based methods in predicting drug-target interaction, as they have shown promising results in this field. These details include the overall framework, main contribution, datasets, and their source codes. The selected papers were mainly published from 2020 to 2024. Prior to discussing papers, we briefly introduce the datasets commonly used with these methods and measurements to assess their performance. Finally, future challenges and some crucial areas that need to be explored are discussed.