Sensor, wearable, and remote patient monitoring technologies are typically used in conjunction with video and/or in-person care for a variety of interventions and care outcomes. This scoping review identifies clinical skills (i.e., competencies) needed to ensure quality care and approaches for organizations to implement and evaluate these technologies. The literature search focused on four concept areas: (1) competencies; (2) sensors, wearables, and remote patient monitoring; (3) mobile, asynchronous, and synchronous technologies; and (4) behavioral health. From 2846 potential references, two authors assessed abstracts for 2828 and, full text for 521, with 111 papers directly relevant to the concept areas. These new technologies integrate health, lifestyle, and clinical care, and they contextually change the culture of care and training—with more time for engagement, continuity of experience, and dynamic data for decision-making for both patients and clinicians. This poses challenges for users (e.g., keeping up, education/training, skills) and healthcare organizations. Based on the clinical studies and informed by clinical informatics, video, social media, and mobile health, a framework of competencies is proposed with three learner levels (novice/advanced beginner, competent/proficient, advanced/expert). Examples are provided to apply the competencies to care, and suggestions are offered on curricular methodologies, faculty development, and institutional practices (e-culture, professionalism, change). Some academic health centers and health systems may naturally assume that clinicians and systems are adapting, but clinical, technological, and administrative workflow—much less skill development—lags. Competencies need to be discrete, measurable, implemented, and evaluated to ensure the quality of care and integrate missions.