The clinical significance of the tumor-immune interaction in breast cancer is now established, and tumor-infiltrating lymphocytes (TILs) have emerged as predictive and prognostic biomarkers for patients with triple-negative (estrogen receptor, progesterone receptor, and HER2-negative) breast cancer and HER2-positive breast cancer. How computational assessments of TILs might complement manual TIL assessment in trial and daily practices is currently debated. Recent efforts to use machine learning (ML) to automatically evaluate TILs have shown promising results. We review state-of-the-art approaches and identify pitfalls and challenges of automated TIL evaluation by studying the root cause of ML discordances in comparison to manual TIL quantification. We categorize our findings into four main topics: (1) technical slide issues, (2) ML and image analysis aspects, (3) data challenges, and (4) validation issues. The main reason for discordant assessments is the inclusion of false-positive areas or cells identified by performance on certain tissue patterns or design choices in the computational implementation. To aid the adoption of ML for TIL assessment, we provide an in-depth discussion of ML and image analysis, including validation issues that need to be considered before reliable computational reporting of TILs can be incorporated into the trial and routine clinical management of patients with triple-negative breast cancer.