The structural health monitoring (SHM) approach plays a key role not only in structural engineering but also in other various engineering disciplines by evaluating the safety and performance monitoring of the structures. The structural damage detection methods could be regarded as the core of SHM strategies. That is because the early detection of the damages and measures to be taken to repair and replace the damaged members with healthy ones could lead to economic advantages and would prevent human disasters. The optimization-based methods are one of the most popular techniques for damage detection. Using these methods, an objective function is minimized by an optimization algorithm during an iterative procedure. The performance of optimization algorithms has a significant impact on the accuracy of damage identification methodology. Hence, a wide variety of algorithms are employed to address optimization-based damage detection problems. Among different algorithms, the particle swarm optimization (PSO) approach has been of the most popular ones. PSO was initially proposed by Kennedy and Eberhart in 1995, and different variants were developed to improve its performance. This work investigates the objectives, methodologies, and results obtained by over 50 studies (2005-2020) in the context of the structural damage detection using PSO and its variants. Then, several important open research questions are highlighted. The paper also provides insights on the frequently used methodologies based on PSO, the computational time, and the accuracy of the existing methodologies.