The convergence of Information Technology (IT), Operational Technology (OT), and Educational Technology (ET) has led to the emergence of the fourth industrial revolution. As a result, a new concept has emerged known as Digital Twins (DT), which is defined as "a virtual representation of various objects or systems that receive data from physical objects/systems to make changes and corrections". In the aviation industry, numerous attempts have been made to utilize DT in the design, manufacturing, and condition monitoring of aircraft fleets. Among these research efforts, real-time, accurate, fast, and predictive condition monitoring methods play a crucial role in ensuring the safe and efficient performance of aircraft. Using DT for condition and fleet monitoring not only enhances the reliability and safety of aircraft but also reduces operational and maintenance costs. In this paper, the conducted studies on the applications of DT systems for condition monitoring of aircraft units and the aerospace sector are discussed and reviewed. The aim of this review paper is to analyse the current developments of DT systems in the aviation industry as well as explain the remaining challenges of DT systems. Then Finally, future trends of DT systems along with aircraft are presented. Among reviewed papers, most of them have used computational fluid dynamics, finite element methods, and artificial intelligence techniques for developing DT models for aircraft. At the same time, most of these analyses are dedicated to the failure and crack detection body of aircraft as well as engine fault detection. Life prediction is another popular application for using DT in aircraft units that could help the engineers predict the maintenance required for different parts of the aircraft. Finally, the application of DT in marine, power systems, and space programs has been also reviewed and the lessons learned from them have been translated to the aviation sector.