Particle swarm optimization (PSO) has evolved significantly since its introduction in 1995. Researchers have developed new versions, applied the technique in various fields, and conducted theoretical studies on its parameters and aspects. This paper provides an overview of PSO from the authors' perspective, including algorithm variations, current research, applications, and open problems. The particle swarm paradigm has gained global interest. This article aims to provide an overview of important work that has guided research in particle swarms, as well as new directions and applications. Due to the fast pace of development in this field, it is impossible to cover all aspects within the page limits. Therefore, this paper serves as a snapshot of the authors' current view. The article is organized as follows. Section 2 explains what particle swarms are and the rules governing their dynamics. Section 3 considers how different social networks influence swarm behavior. Section 4 reviews interesting variants of PSO. Section 5 summarizes theoretical analyses of PSO. Section 6 discusses successful applications of particle swarms. Section 7 lists and discusses open problems in PSO. Section 8 draws conclusions. In PSO, particles are simple entities placed in a search space. Each particle evaluates the objective function at its current location. The particle's movement is determined by combining its own history and the history of other particles in the swarm, with some random perturbations. The next iteration occurs after all particles have moved. Eventually, the swarm as a whole is likely to move close to an optimum of the fitness function. Each particle has three D-dimensional vectors: current position, previous best position, and velocity. The current position is evaluated as a solution. If it is better than previous solutions, it is stored in the previous best position vector. The best function result is stored in a variable for later comparison. The objective is to find better positions and update the previous best position and best function result. New points are generated by adding velocity coordinates to the current position. The algorithm adjusts velocity, which can be seen as a step size. The particle swarm is more than just a collection of particles. A particle alone has little power to solve a problem; progress occurs only when particles interact.Particle swarm optimization (PSO) has evolved significantly since its introduction in 1995. Researchers have developed new versions, applied the technique in various fields, and conducted theoretical studies on its parameters and aspects. This paper provides an overview of PSO from the authors' perspective, including algorithm variations, current research, applications, and open problems. The particle swarm paradigm has gained global interest. This article aims to provide an overview of important work that has guided research in particle swarms, as well as new directions and applications. Due to the fast pace of development in this field, it is impossible to cover all aspects within the page limits. Therefore, this paper serves as a snapshot of the authors' current view. The article is organized as follows. Section 2 explains what particle swarms are and the rules governing their dynamics. Section 3 considers how different social networks influence swarm behavior. Section 4 reviews interesting variants of PSO. Section 5 summarizes theoretical analyses of PSO. Section 6 discusses successful applications of particle swarms. Section 7 lists and discusses open problems in PSO. Section 8 draws conclusions. In PSO, particles are simple entities placed in a search space. Each particle evaluates the objective function at its current location. The particle's movement is determined by combining its own history and the history of other particles in the swarm, with some random perturbations. The next iteration occurs after all particles have moved. Eventually, the swarm as a whole is likely to move close to an optimum of the fitness function. Each particle has three D-dimensional vectors: current position, previous best position, and velocity. The current position is evaluated as a solution. If it is better than previous solutions, it is stored in the previous best position vector. The best function result is stored in a variable for later comparison. The objective is to find better positions and update the previous best position and best function result. New points are generated by adding velocity coordinates to the current position. The algorithm adjusts velocity, which can be seen as a step size. The particle swarm is more than just a collection of particles. A particle alone has little power to solve a problem; progress occurs only when particles interact.