With the advances in machine learning (ML) and deep learning (DL) techniques, and the potency of cloud computing in offering services efficiently and cost-effectively, Machine Learning as a Service (MLaaS) cloud platforms have become popular. In addition, there is increasing adoption of third-party cloud services for outsourcing training of DL models, which requires substantial costly computational resources (e.g., high-performance graphics processing units (GPUs)). Such widespread usage of cloud-hosted ML/DL services opens a wide range of attack surfaces for adversaries to exploit the ML/DL system to achieve malicious goals. In this article, we conduct a systematic evaluation of literature of cloud-hosted ML/DL models along both the important dimensions—attacks and defenses—related to their security. Our systematic review identified a total of 31 related articles out of which 19 focused on attack, six focused on defense, and six focused on both attack and defense. Our evaluation reveals that there is an increasing interest from the research community on the perspective of attacking and defending different attacks on Machine Learning as a Service platforms. In addition, we identify the limitations and pitfalls of the analyzed articles and highlight open research issues that require further investigation.