With the advancement of Machine Learning, since its beginning and over the last years, a special attention has been given to the Artificial Neural Network. As an inspiration from natural selection of animal groups and human’s neural system, the Artificial Neural Network also known as Neural Networks has become the new computational power which is used for solving real world problems. Neural Networks alone as a concept involve various methods for achieving their success; thus, this review paper describes an overview of such methods called Particle Swarm Optimization, Backpropagation, and Neural Network itself, respectively. A brief explanation of the concepts, history, performances, advantages, and disadvantages is given, followed by the latest researches done on these methods. A description of solutions and applications on various industrial sectors such as Medicine or Information Technology has been provided. The last part briefly discusses the directions, current, and future challenges of Neural Networks towards achieving the highest success rate in solving real world problems.