Cancer is a fatal illness frequently caused by a variety of obsessive changes and genetic disorders. Cancer cells knowing as abnormal cells can grow in any part of the human body. A preliminary diagnosis of cancer is necessary as cancer is one of the most alarming diseases. Detecting cancer and treating it in the initial stage can decrease the death rate. Our aim of this study is to analyze and review various relevant research papers published over the last 5 years for cancer detection using Machine Learning (ML) and Deep Learning (DL) techniques. We have mainly considered the techniques developed for Brain Tumor detection, Cervical Cancer detection, Breast Cancer detection, Skin Cancer detection and Lung Cancer detection. Recent statistics show that these cancers are causing higher mortality rates among men and women in comparison to the other types of cancers. In this review article, various recent ML and DL models developed to detect these cancers are analyzed and discussed on the most important metrics such as accuracy, specificity, sensitivity, F-score, precision, recall etc. which are tested on several datasets in the literature. At last, open research challenges in each cancer category are also pointed out for the purpose of future research work opportunities.