The future Internet of Things (IoT) will have a deep economical, commercial and social impact on our lives. The participating nodes in IoT networks are usually resource-constrained, which makes them luring targets for cyber attacks. In this regard, extensive efforts have been made to address the security and privacy issues in IoT networks primarily through traditional cryptographic approaches. However, the unique characteristics of IoT nodes render the existing solutions insufficient to encompass the entire security spectrum of the IoT networks. Machine Learning (ML) and Deep Learning (DL) techniques, which are able to provide embedded intelligence in the IoT devices and networks, can be leveraged to cope with different security problems. In this paper, we systematically review the security requirements, attack vectors, and the current security solutions for the IoT networks. We then shed light on the gaps in these security solutions that call for ML and DL approaches. Finally, we discuss in detail the existing ML and DL solutions for addressing different security problems in IoT networks. We also discuss several future research directions for ML- and DL-based IoT security.