Drugs refer to the chemical compounds that are consumed by the human body and induce a change by interacting with the protein targets. The drugs may induce favorable or unfavorable changes in the human body. The unfavorable changes that are elicited by the drugs in the human body are known as drug side effects. These side effects range from minor reactions like headache to serious reactions such as cardiac arrest, cancer, or even death. The drugs are tested for their side effects based on laboratory experiments. However, these experiments are costly as well as prolonged. An alternative to the laboratory experiments is provided through the computational methods. Many computational techniques for identifying the drug side effects have been developed in the recent past. This review aims to summarize the important studies and contributions in the field of drug side effect prediction by computational techniques. A description of the data sets related to drug side effects and the metrics used for the evaluation of drug side effect prediction methods have also been explained. This article also highlights the future research that can be undertaken in this field. To the best of our knowledge, this is the first extensive review of the computational methods that have been developed for drug side effect prediction.