To promote secure and private artificial intelligence (SPAI), we review studies on the model security and data privacy of DNNs. Model security allows system to behave as intended without being affected by malicious external influences that can compromise its integrity and efficiency. Security attacks can be divided based on when they occur: if an attack occurs during training, it is known as a poisoning attack, and if it occurs during inference (after training) it is termed an evasion attack. Poisoning attacks compromise the training process by corrupting the data with malicious examples, while evasion attacks use adversarial examples to disrupt entire classification process. Defenses proposed against such attacks include techniques to recognize and remove malicious data, train a model to be insensitive to such data, and mask the model's structure and parameters to render attacks more challenging to implement. Furthermore, the privacy of the data involved in model training is also threatened by attacks such as the model-inversion attack, or by dishonest service providers of AI applications. To maintain data privacy, several solutions that combine existing data-privacy techniques have been proposed, including differential privacy and modern cryptography techniques. In this paper, we describe the notions of some of methods, e.g., homomorphic encryption, and review their advantages and challenges when implemented in deep-learning models.