The use of mobile, wearable, and Internet of Things (IoT) technologies fosters unique opportunities for designing novel intelligent positive computing services that address various health and well-being issues such as stress and depression. As positive computing research is often cross-disciplinary, it is difficult to acquire holistic perspectives on the design, implementation, and evaluation of intelligent positive computing systems with mobile, wearable, and IoT technologies. To bridge this gap, we propose a conceptual framework and review the key components to provide guidelines for intelligent positive computing systems research. We also present several practical service scenarios and provide useful insights on opportunities and challenges. By critically reflecting on the literature and scenarios, we suggest several research directions on the core topics in intelligent positive computing systems research. In addition, we discuss concerns and challenges such as technology dependence, abandonment, side effects, privacy, and ethical issues.