Traditional histopathology, characterized by manual quantifications and assessments, faces challenges such as low-throughput and inter-observer variability that hinder the introduction of precision medicine in pathology diagnostics and research. The advent of digital pathology allowed the introduction of computational pathology, a discipline that leverages computational methods, especially based on deep learning (DL) techniques, to analyze histopathology specimens. A growing body of research shows impressive performances of DL-based models in pathology for a multitude of tasks, such as mutation prediction, large-scale pathomics analyses, or prognosis prediction. New approaches integrate multimodal data sources and increasingly rely on multi-purpose foundation models. This review provides an introductory overview of advancements in computational pathology and discusses their implications for the future of histopathology in research and diagnostics.