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Data-driven model with predictive ability are important to be used in medical and healthcare. However, the most challenging task in predictive modeling is to construct a prediction model, which can be addressed using machine learning (ML) methods. The methods are used to learn and trained the model using a gene expression dataset without being programmed explicitly. Due to the vast amount of gene expression data, this task becomes complex and time consuming. This paper provides a recent review on recent progress in ML and deep learning (DL) for cancer classification, which has received increasing attention in bioinformatics and computational biology. The development of cancer classification methods based on ML and DL is mostly focused on this review. Although many methods have been applied to the cancer classification problem, recent progress shows that most of the successful techniques are those based on supervised and DL methods. In addition, the sources of the healthcare dataset are also described. The development of many machine learning methods for insight analysis in cancer classification has brought a lot of improvement in healthcare. Currently, it seems that there is highly demanded further development of efficient classification methods to address the expansion of healthcare applications.