COVID-19 is the disease evoked by a new breed of coronavirus called the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Recently, COVID-19 has become a pandemic by infecting more than 152 million people in over 216 countries and territories. The exponential increase in the number of infections has rendered traditional diagnosis techniques inefficient. Therefore, many researchers have developed several intelligent techniques, such as deep learning (DL) and machine learning (ML), which can assist the healthcare sector in providing quick and precise COVID-19 diagnosis. Therefore, this paper provides a comprehensive review of the most recent DL and ML techniques for COVID-19 diagnosis. The studies are published from December 2019 until April 2021. In general, this paper includes more than 200 studies that have been carefully selected from several publishers, such as IEEE, Springer and Elsevier. We classify the research tracks into two categories: DL and ML and present COVID-19 public datasets established and extracted from different countries. The measures used to evaluate diagnosis methods are comparatively analysed and proper discussion is provided. In conclusion, for COVID-19 diagnosing and outbreak prediction, SVM is the most widely used machine learning mechanism, and CNN is the most widely used deep learning mechanism. Accuracy, sensitivity, and specificity are the most widely used measurements in previous studies. Finally, this review paper will guide the research community on the upcoming development of machine learning for COVID-19 and inspire their works for future development. This review paper will guide the research community on the upcoming development of ML and DL for COVID-19 and inspire their works for future development.