Immunotherapy deals with therapeutic interventions to arrest the progression of tumours using the immune system. These include checkpoint inhibitors, T-cell manipulation, cytokines, oncolytic viruses and tumour vaccines. In this paper, we present a survey of the latest developments on immunotherapy in colorectal cancer (CRC) and the role of artificial intelligence (AI) in this context. Among these, microsatellite instability (MSI) is perhaps the most popular IO biomarker globally. We first discuss the MSI status of tumours, its implications for patient management, and its relationship to immune response. In recent years, several aspiring studies have used AI to predict the MSI status of patients from digital whole-slide images (WSIs) of routine diagnostic slides. We present a survey of AI literature on the prediction of MSI and tumour mutation burden from digitised WSIs of haematoxylin and eosin-stained diagnostic slides. We discuss AI approaches in detail and elaborate their contributions, limitations and key takeaways to drive future research. We further expand this survey to other IO-related biomarkers like immune cell infiltrates and alternate data modalities like immunohistochemistry and gene expression. Finally, we underline possible future directions in immunotherapy for CRC and promise of AI to accelerate this exploration for patient benefits.