Malware is one of the most common and severe cyber-attack today. Malware infects millions of devices and can perform several malicious activities including mining sensitive data, encrypting data, crippling system performance, and many more. Hence, malware detection is crucial to protect our computers and mobile devices from malware attacks. Deep learning (DL) is one of the emerging and promising technologies for detecting malware. The recent high production of malware variants against desktop and mobile platforms makes DL algorithms powerful approaches for building scalable and advanced malware detection models as they can handle big datasets. This work explores current deep learning technologies for detecting malware attacks on the Windows, Linux, and Android platforms. Specifically, we present different categories of DL algorithms, network optimizers, and regularization methods. Different loss functions, activation functions, and frameworks for implementing DL models are presented. We also present feature extraction approaches and a review of recent DL-based models for detecting malware attacks on the above platforms. Furthermore, this work presents major research issues on malware detection including future directions to further advance knowledge and research in this field.