The exponential growth of big data and deep learning has increased the data exchange traffic in society. Machine Learning as a Service, (MLaaS) which leverages deep learning techniques for predictive analytics to enhance decision-making, has become a hot commodity. However, the adoption of MLaaS introduces data privacy challenges for data owners and security challenges for deep learning model owners. Data owners are concerned about the safety and privacy of their data on MLaaS platforms, while MLaaS platform owners worry that their models could be stolen by adversaries who pose as clients. Consequently, Privacy-Preserving Deep Learning (PPDL) arises as a possible solution to this problem. Recently, several papers about PPDL for MLaaS have been published. However, to the best of our knowledge, no previous paper has summarized the existing literature on PPDL and its specific applicability to the MLaaS environment. In this paper, we present a comprehensive survey of privacy-preserving techniques, starting from classical privacy-preserving techniques to well-known deep learning techniques. Additionally, we present a detailed description of PPDL and address the issue of using PPDL for MLaaS. Furthermore, we undertake detailed comparisons between state-of-the-art PPDL methods. Subsequently, we classify an adversarial model on PPDL by highlighting possible PPDL attacks and their potential solutions. Ultimately, our paper serves as a single point of reference for detailed knowledge on PPDL and its applicability to MLaaS environments for both new and experienced researchers.