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Precision health leverages information from various sources, including omics, lifestyle, environment, social media, medical records, and medical insurance claims to enable personalized care, prevent and predict illness, and precise treatments. It extensively uses sensing technologies (e.g., electronic health monitoring devices), computations (e.g., machine learning), and communication (e.g., interaction between the health data centers). As health data contain sensitive private information, including the identity of patient and carer and medical conditions of the patient, proper care is required at all times. Leakage of these private information affects the personal life, including bullying, high insurance premium, and loss of job due to the medical history. Thus, the security, privacy of and trust on the information are of utmost importance. Moreover, government legislation and ethics committees demand the security and privacy of healthcare data. Herein, in the light of precision health data security, privacy, ethical and regulatory requirements, finding the best methods and techniques for the utilization of the health data, and thus precision health is essential. In this regard, firstly, this paper explores the regulations, ethical guidelines around the world, and domain-specific needs. Then it presents the requirements and investigates the associated challenges. Secondly, this paper investigates secure and privacy-preserving machine learning methods suitable for the computation of precision health data along with their usage in relevant health projects. Finally, it illustrates the best available techniques for precision health data security and privacy with a conceptual system model that enables compliance, ethics clearance, consent management, medical innovations, and developments in the health domain.