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Scalar fields are a useful proxy for other complex interactions, but also an attractive extension of General Relativity and a possible dark matter component. I will discuss some aspects of the gravitational interaction of scalar fields, in particular (i) the formation and growth of self-gravitating structures and their interaction with compact stars. and (ii) superradiance around black holes and how it can be used to constraint particle masses.

An algebraic view allows one to compute properties of physical states without having to introduce an explicit Hilbert space. In relational systems without absolute time, a state cannot be completely positive once a choice for a (possibly local) internal time has been made. A more general class of `almost-positive' states is introduced in this talk, together with a discussion of their constrained dynamics.