Deep Learning (DL), a novel form of machine learning (ML) is gaining much research interest due to its successful application in many classical artificial intelligence (AI) tasks as compared to classical ML algorithms (CMLAs). Recently, DL architectures are being innovatively modelled for diverse applications in the area of cyber security. The literature is now growing with DL architectures and their variations for exploring different innovative DL models and prototypes that can be tailored to suit specific cyber security applications. However, there is a gap in literature for a comprehensive survey reporting on such research studies. Many of the survey-based research have a focus on specific DL architectures and certain types of malicious attacks within a limited cyber security problem scenario of the past and lack futuristic review. This paper aims at providing a well-rounded and thorough survey of the past, present, and future DL architectures including next-generation cyber security scenarios related to intelligent automation, Internet of Things (IoT), Big Data (BD), Blockchain, cloud and edge technologies. This paper presents a tutorial-style comprehensive review of the state-of-the-art DL architectures for diverse applications in cyber security by comparing and analysing the contributions and challenges from various recent research papers. Firstly, the uniqueness of the survey is in reporting the use of DL architectures for an extensive set of cybercrime detection approaches such as intrusion detection, malware and botnet detection, spam and phishing detection, network traffic analysis, binary analysis, insider threat detection, CAPTCHA analysis, and steganography. Secondly, the survey covers key DL architectures in cyber security application domains such as cryptography, cloud security, biometric security, IoT and edge computing. Thirdly, the need for DL based research is discussed for the next generation cyber security applications in cyber physical systems (CPS) that leverage on BD analytics, natural language processing (NLP), signal and image processing and blockchain technology for smart cities and Industry 4.0 of the future. Finally, a critical discussion on open challenges and new proposed DL architecture contributes towards future research directions.