The expansion of Internet of Things (IoT) devices across diverse domains has led to the generation of an enormous amount of sensitive data. While IoT networks have been extensively studied for their security vulnerabilities, privacy concerns have emerged as a critical issue, particularly in scenarios involving sensitive data, such as smart healthcare. Simultaneously, the rich data ecosystem of IoT devices has enabled their integration with machine learning (ML) and deep learning (DL), adding obstacles to protecting private data. This paper investigates the state-of-the-art methods for privacy-preserving deep learning (PPDL) in IoT systems, focusing on two key scenarios: DL-as-a-Service and collaborative learning. We evaluate existing privacy-preserving technologies regarding their practical applicability for IoT devices. Our study identifies strengths, limitations, and gaps in the current methods, offering insights into their deployment feasibility in resource-constrained environments. Our analysis highlights the underrepresentation of PPDL technologies tailored to IoT applications and key challenges to overcome, such as stalled research efforts and suboptimal privacy-utility tradeoffs. We also highlight future research directions to address these challenges, ensuring the development of robust and scalable PPDL solutions.