Artificial intelligence and machine learning (AI/ML) technologies offer unique opportunities to transform nuclear plant operations and power generation. Benefits will be felt not only within existing analog and digital instrumentation and control, but also within work processes, the integration of people with technology and most importantly, the business case. The application of this new technology can help simplify complex problems and produce more effective decision-making, making nuclear power safer, more efficient, and more economically viable in the current energy market. Nonetheless, there are potential barriers to its adoption that must be overcome. The purpose of this paper is to categorize, review, and discuss barriers to AI/ML adoption within the nuclear power industry, with a focus on existing commercial reactors. Unique considerations for advanced reactors are also offered. We provide a comprehensive overview of the historical, technical, and business barriers that the industry faces, as well as stakeholder readiness, and end-user acceptance. We underscore the importance of user experience and offer potential solutions in overcoming each barrier. These include provisions for easier plant data access, a friendly regulatory environment, and investment in user trust and explainable AI.