Shape memory alloys (SMAs) are a class of functional materials with the ability to regain their original shapes after a large inelastic deformation upon external stimuli. In recent years, SMAs have been employed in many applications in different fields. Nitinol is the most widely used SMA due to its outstanding properties such as shape memory effect, superelasticity, biocompatibility, and corrosion resistance among other types of SMAs. Some efforts are also made to implement SMAs on filtration devices that require deployable structures. This motivates the authors to write a review of the recent developments in the field of SMA based filtration devices as far as the use of SMAs is concerned. The present work provides a brief overview of history and basics of SMAs. This paper then reviews and discusses the recent progress and applications of SMA based filtration devices and the challenges of these filtration devices. It is found that most devices are made of nitinol. The aim of this paper is to introduce SMA based filtration devices and promote future developments of functional filtration applications.