  The interaction of quantum light with matter is of great importance to a wide
range of scientific disciplines, ranging from optomechanics to high precision
measurements. A central issue we discuss here, is how to make optimal use of
both the spatial and the quantum degrees of freedom of light for characterizing
and manipulating arbitrary observable parameters in a linear scattering system
into which suitably engineered light fields are injected. Here, we discuss a
comprehensive framework based on a quantum operator that can be assembled
solely from the scattering matrix of a system and its dependence on the
corresponding local parameter, making this operator experimentally measurable
from the far-field using only classical light. From this, the effect of quantum
light in the near-field, i.e., in the vicinity of the target object, can be
inferred. Based on this framework, it is straightforward to formulate optimal
protocols on how to jointly design both the spatial shape and the quantum
characteristics of light for micromanipulation as well as for parameter
estimation in arbitrarily complex media. Also the forces of the quantum vacuum
naturally emerge from this formalism. The aim of our tutorial is to bring
different perspectives into alignment and thereby build a bridge between the
different communities of wave control, quantum optics, micromanipulation,
quantum metrology and vacuum physics.
