In many oil reservoirs worldwide, the downhole pressure does not have the ability to lift the produced fluids to the surface. In order to produce these fluids, pumps are used to artificially lift the fluids; this method is referred to as artificial lift. More than seventy percent of all currently producing oil wells are being produced by artificial lift methods. One of the most applied artificial lift methods is sucker rod pump. Sucker rod pumps are considered a well-established technology in the oil and gas industry and thus are easy to apply, very common worldwide, and low in capital and operational costs. Many advancements in technology have been applied to improve sucker rod pumps performance, applicability range, and diagnostics. With these advancements, it is important to be able to constantly provide an updated review and guide to the utilization of the sucker rod pumps. This research provides an updated comprehensive review of sucker rod pumps components, diagnostics methods, mathematical models, and common failures experienced in the field and how to prevent and mitigate these failures. Based on the review conducted, a new classification of all the methods that can fall under the sucker rod pump technology based on newly introduced sucker rod pump methods in the industry has been introduced. Several field cases studies from wells worldwide are also discussed in this research to highlight some of the main features of sucker rod pumps. Finally, the advantages and limitations of sucker rod pumps are mentioned based on the updated review. The findings of this study can help increase the understanding of the different sucker rod pumps and provide a holistic view of the beam rod pump and its properties and modeling.