  Conventional approaches for controlling open quantum systems use coherent
control which affects the system's evolution through the Hamiltonian part of
the dynamics. Such control, although being extremely efficient for a large
variety of problems, has limited capabilities, e.g., if the initial and desired
target states have density matrices with different spectra or if a control
field needs to be designed to optimally transfer different initial states to
the same target state. Recent research works suggest extending coherent control
by including active manipulation of the non-unitary (i.e., incoherent) part of
the evolution. This paper summarizes recent results specifically for incoherent
control by the environment (e.g., incoherent radiation or a gaseous medium)
with a kinematic description of controllability and landscape analysis.
