The concept of sensor networks (WSNs) has become an important component of the recently proposed cyber-physical systems (CPSs) and Internet of Things which can connect the physical world with embedded software systems. Energy- harvesting (EH) as an enabling technology applied in SNs can heavily reduce the installation and maintenance cost as well as increase system life, flexibility, and scalability as the EH is subject to the important "energy interruption" problem where system tasks can be significantly disrupted by the EH outputs. This problem not only affects the system modeling but also relates to the cross-layer network design and schedulability. This paper discusses the EH-powered CPS architecture and some theoretical problems. In particular, we propose a framework for fully EH-powered CPS, within which essential topics are discussed, such as EH software architecture, EH models, and real-time communication. Different EH models for CPSs (e.g., fully EH-powered and partially EH-powered) are addressed. Future research directions are briefly discussed in the end.