Recent advances in deep learning have completely transformed the domain of computational pathology (CPath), which in turn altered the diagnostic workflow of pathologists by integrating foundation models (FMs) and vision-language models (VLMs) in their assessment and decision-making process. FMs overcome the limitations of existing deep learning approaches in CPath by learning a representation space that can be adapted to a wide variety of downstream tasks without explicit supervision. VLMs allow pathology reports written in natural language to be used as a rich semantic information source to improve existing models as well as generate predictions in natural language form. In this survey, a holistic and systematic overview of recent innovations in FMs and VLMs in CPath is presented. Furthermore, the tools, datasets and training schemes for these models are summarized in addition to categorizing them into distinct groups. This extensive survey highlights the current trends in CPath and the way it is going to be transformed through FMs and VLMs in the future.