The extent of tumor-infiltrating lymphocytes (TILs), along with immunomodulatory ligands, tumor-mutational burden and other biomarkers, has been demonstrated to be a marker of response to immune-checkpoint therapy in several cancers. Pathologists have therefore started to devise standardized visual approaches to quantify TILs for therapy prediction. However, despite successful standardization efforts visual TIL estimation is slow, with limited precision and lacks the ability to evaluate more complex properties such as TIL distribution patterns. Therefore, computational image analysis approaches are needed to provide standardized and efficient TIL quantification. Here, we discuss different automated TIL scoring approaches ranging from classical image segmentation, where cell boundaries are identified and the resulting objects classified according to shape properties, to machine learning-based approaches that directly classify cells without segmentation but rely on large amounts of training data. In contrast to conventional machine learning (ML) approaches that are often criticized for their "black-box" characteristics, we also discuss explainable machine learning. Such approaches render ML results interpretable and explain the computational decision-making process through high-resolution heatmaps that highlight TILs and cancer cells and therefore allow for quantification and plausibility checks in biomedical research and diagnostics.