With the fast-paced development of artificial intelligence (AI) and deep learning, intelligent surveillance systems have taken center stage for enhancing public safety and deterring crime. Classical CCTV systems, which are dependent on human observation of the video, are likely to fail, make mistakes, and consume a lot of resources. This review paper explores how the current deep learning techniques such as Convolutional Neural Networks (CNNs), Long Short-Term Memory (LSTM) networks, Vision Transformers, and YOLO-based models are revolutionizing surveillance to enable real-time accurate detection of violence, theft, loitering, and weapons. We compare traditional surveillance systems, machine learning-based systems, and deep learning-based systems. We compare performance parameters such as accuracy, speed, and real-world adoption. We compare datasets, model architecture, and applications where these systems are applied. We discuss important concerns such as data privacy, algorithmic bias, and ethical concerns. We also discuss how edge computing and IoT technologies facilitate the creation of smart surveillance solutions that are scalable and responsive. This survey demonstrates that deep learning models are significantly superior to conventional approaches in terms of accuracy and automation. But to apply these models extensively, we require responsible AI development, privacy-respecting designs, and more stringent rules and regulations. This paper would like to assist future research to develop intelligent, ethical, and efficient surveillance systems for public safety.