Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2), causing a disease called COVID-19, is a class of acute respiratory syndrome that has considerably affected the global economy and healthcare system. This virus is diagnosed using a traditional technique known as the Reverse Transcription Polymerase Chain Reaction (RT-PCR) test. However, RT-PCR customarily outputs a lot of false-negative and incorrect results. Current works indicate that COVID-19 can also be diagnosed using imaging resolutions, including CT scans, X-rays, and blood tests. Nevertheless, X-rays and CT scans cannot always be used for patient screening because of high costs, radiation doses, and an insufficient number of devices. Therefore, there is a requirement for a less expensive and faster diagnostic model to recognize the positive and negative cases of COVID-19. Blood tests are easily performed and cost less than RT-PCR and imaging tests. Since biochemical parameters in routine blood tests vary during the COVID-19 infection, they may supply physicians with exact information about the diagnosis of COVID-19. This study reviewed some newly emerging artificial intelligence (AI)-based methods to diagnose COVID-19 using routine blood tests. We gathered information about research resources and inspected 92 articles that were carefully chosen from a variety of publishers, such as IEEE, Springer, Elsevier, and MDPI. Then, these 92 studies are classified into two tables which contain articles that use machine Learning and deep Learning models to diagnose COVID-19 while using routine blood test datasets. In these studies, for diagnosing COVID-19, Random Forest and logistic regression are the most widely used machine learning methods and the most widely used performance metrics are accuracy, sensitivity, specificity, and AUC. Finally, we conclude by discussing and analyzing these studies which use machine learning and deep learning models and routine blood test datasets for COVID-19 detection. This survey can be the starting point for a novice-/beginner-level researcher to perform on COVID-19 classification.