Fault tolerance is crucial in ensuring smooth working of distributed and cloud computing. It is challenging to implement because of the constantly changing infrastructure and complex configurations in distributed and cloud computing. Implementation of various fault tolerance methods require domain‐specific knowledge as well as in‐depth understanding of the existing techniques and approaches. Recent surveys on fault tolerance in cloud and distributed environments exist, but they have limitations. This article systematically reviews fault tolerance approaches in distributed and cloud computing and discusses their taxonomy. Based on the taxonomy provided, fault‐tolerance approaches are divided into four types, that is, reactive approaches, proactive approaches, adaptive approaches, and hybrid approaches. Reactive approaches provide a preventive measure after the occurrence of faults in the system. Proactive approaches prevent the system or minimize failure effects by predicting in advance. The adaptive approaches predict, learn, and adapt the changes to deal with new faults in the system. The hybrid approaches combine reactive, proactive, and adaptive approaches. The objective of this article is to give a better understanding of handling faults using suitable approaches and further compare them on various parameters. The paper also presents a promising research direction based on the challenges and issues in multiple approaches.