Crowd counting system has gained significant attention in recent years due to its relevance in various domains such as urban planning, public safety, resource allocation and decision-making in crowded environments. Due to differences in crowd densities, occlusions, size changes, and perspective distortions that are frequently seen in realworld scenarios, the system, nevertheless, falls short in terms of its purpose. To address this, it is necessary to create advanced neural network architectures, efficient methods for gathering and annotating data, reliable training procedures, and assessment criteria that accurately reflect the effectiveness of crowd counting systems. Therefore, the purpose of this study is to provide a comprehensive review of the state of the art in neural network-based crowd counting systems. The developments in neural network based crowd counting procedures, along with their features and limitations, most widely datasets and evaluation criteria are explored. The experimental findings of recent crowd counting systems are also examined. Hence, this work serves as an inspiration for additional research and development in this area, ultimately advancing crowd analysis and management systems.