In this work, we provide an industry research view for approaching the design, deployment, and operation of trustworthy Artificial Intelligence (AI) inference systems. Such systems provide customers with timely, informed, and customized inferences to aid their decision, while at the same time utilizing appropriate security protection mechanisms for AI models. Additionally, such systems should also use Privacy-Enhancing Technologies (PETs) to protect customers' data at any time. To approach the subject, we start by introducing current trends in AI inference systems. We continue by elaborating on the relationship between Intellectual Property (IP) and private data protection in such systems. Regarding the protection mechanisms, we survey the security and privacy building blocks instrumental in designing, building, deploying, and operating private AI inference systems. For example, we highlight opportunities and challenges in AI systems using trusted execution environments combined with more recent advances in cryptographic techniques to protect data in use. Finally, we outline areas of further development that require the global collective attention of industry, academia, and government researchers to sustain the operation of trustworthy AI inference systems.