The treatment and diagnosis of colon cancer are considered to be social and economic challenges due to the high mortality rates. Every year, around the world, almost half a million people contract cancer, including colon cancer. Determining the grade of colon cancer mainly depends on analyzing the gland's structure by tissue region, which has led to the existence of various tests for screening that can be utilized to investigate polyp images and colorectal cancer. This article presents a comprehensive survey on the diagnosis of colon cancer. This covers many aspects related to colon cancer, such as its symptoms and grades as well as the available imaging modalities (particularly, histopathology images used for analysis) in addition to common diagnosis systems. Furthermore, the most widely used datasets and performance evaluation metrics are discussed. We provide a comprehensive review of the current studies on colon cancer, classified into deep-learning (DL) and machine-learning (ML) techniques, and we identify their main strengths and limitations. These techniques provide extensive support for identifying the early stages of cancer that lead to early treatment of the disease and produce a lower mortality rate compared with the rate produced after symptoms develop. In addition, these methods can help to prevent colorectal cancer from progressing through the removal of pre-malignant polyps, which can be achieved using screening tests to make the disease easier to diagnose. Finally, the existing challenges and future research directions that open the way for future work in this field are presented.