Interaction with cyber-physical systems (CPSs) is a new challenge for system developers and human-system interaction designers, and but also for end-users. Due to the lack of proper insights, there are many unknowns, open issues, and eventually new challenges. For this reason, there is a need for a comprehensive theory that considers all aspects of interaction with CPSs, provides a reasoning framework, and facilitates the implementation of highly interactive CPSs. The research presented in this paper tries to make the first steps in this direction. We are aware of the fact that, in the case of CPSs, system-human interaction and system-system interaction are to be considered besides human-system interaction. Human-system interaction influenced by: (i) the level of interaction, (ii) the intellectual domains of interaction, (iii) the contexts of interaction, and (iv) the modalities of interaction. The proposed theory decomposes these into various constituents and captures the relations among them. Physical, syntactic, semantic, semantic, pragmatic and apobetic levels of interaction are considered in combination with four domains of interaction (perceptive, cognitive, motor, and emotional). In addition to the common human interaction modalities (visual, audio, haptic, etc.), the theory also considers system communication channels. It is claimed that interaction is also influenced by the implicit context implied by the specific objectives of interaction, i.e., cooperation, coordination, collaboration of coadunation, and not only by the explicit context provided by narrower and broader embedding environments of CPSs. The theory establishes explicit relationships between the above mentioned influencing factors, which are important at specifying wishful interaction profiles. The advantages that the proposed comprehensive theory offers in comparison with the traditional interaction design approaches are shown through the example of a smart bathroom.@en