Recent theoretical and practical studies have revealed that malware is one of the most harmful threats to the digital world. Malware mitigation techniques have evolved over the years to ensure security. Earlier, several classical methods were used for detecting malware embedded with various features like the signature, heuristic, and others. Traditional malware detection techniques were unable to defeat new generations of malware and their sophisticated obfuscation tactics. Deep Learning is increasingly used in malware detection as DL-based systems outperform conventional malware detection approaches at finding new malware variants. Furthermore, DL-based techniques provide rapid malware prediction with excellent detection rates and analysis of different malware types. Investigating recently proposed Deep Learning-based malware detection systems and their evolution is hence of interest to this work. It offers a thorough analysis of the recently developed DL-based malware detection techniques. Furthermore, current trending malwares are studied and detection techniques of Mobile malware (both Android and iOS), Windows malware, IoT malware, Advanced Persistent Threats (APTs), and Ransomware are precisely reviewed.