This paper considers the general H8 optimal control problem from a behavioral perspective. A formalization of this problem is given that departs from the usual H8 control paradigm in the sense that system variables of the plant are treated in a symmetric way, without distinguishing control inputs, measurements, exogenous inputs and to-be-controlled variables. Interconnection variables are introduced and controllers are allowed to constrain the interconnection variables of the plant. Necessary and sufficient conditions are given for the existence of controllers that achieve an H8 control objective for a given linear time-invariant plant. The set of all such controllers is parametrized by means of J-spectral factorizations.