Liver cancer is a malignant liver tumor that originates from liver cells, and its diagnosis has always been a difficult medical problem and a research hotspot in various fields. Early diagnosis of liver cancer can reduce the mortality rate of liver cancer. Histopathological image examination is the gold standard for oncology diagnosis as the images can display the cells and tissue structures of tissue slices, which can be employed to determine cell types, tissue structures, and the number and morphology of abnormal cells, and evaluate the specific condition of the tumor. This study focuses on the application of convolutional neural networks in liver cancer diagnosis algorithms for pathological images, including liver tumor detection, image segmentation, and preoperative prediction. The design ideas and related improvement goals and methods of each algorithm of convolutional neural networks are elaborated in detail to provide clearer reference ideas for researchers. Additionally, the advantages and disadvantages of convolutional neural network algorithms in diagnosis are summarized and analyzed, with potential research hotspots and related difficulties in the future discussed.