Software reliability, a cornerstone in software engineering, has gained renewed attention with the emergence of artificial intelligence (AI), spotlighting the significance of AI software reliability. Scholars and researchers have now begun to cast a discerning eye on this nascent yet paramount domain. This paper delves into the foundational research of AI software reliability, encompassing its essence - defined by specified time, conditions, and functionality - and its related domains, including uncertainties, generalization, and other factors. Our work presents a structured elucidation of the concept of reliability in AI software systems, offering clarity on its intrinsic and extrinsic aspects. In conclusion, this study underscores the impending challenges in the domain of AI reliability, pointing towards the intricate task ahead for researchers and practitioners.