The escalating apprehension surrounding the carcinogenic potential of chemicals emphasizes the imperative need for efficient methods of assessing carcinogenicity. Conventional experimental approaches such as in vitro and in vivo assays, albeit effective, suffer from being costly and time-consuming. In response to this challenge, new alternative methodologies, notably machine learning and deep learning techniques, have attracted attention for their potential in developing carcinogenicity prediction models. This article reviews the progress in predicting carcinogenicity using various machine learning and deep learning algorithms. A comparative analysis on these developed models reveals that support vector machine, random forest, and ensemble learning are commonly preferred for their robustness and effectiveness in predicting chemical carcinogenicity. Conversely, models based on deep learning algorithms, such as feedforward neural network, convolutional neural network, graph convolutional neural network, capsule neural network, and hybrid neural networks, exhibit promising capabilities but are limited by the size of available carcinogenicity datasets. This review provides a comprehensive analysis of current machine learning and deep learning models for carcinogenicity prediction, underscoring the importance of high-quality and large datasets. These observations are anticipated to catalyze future advancements in developing effective and generalizable machine learning and deep learning models for predicting chemical carcinogenicity.