  We discuss models of ultralight scalar Dark Matter (DM) with linear and
quadratic couplings to the Standard Model (SM). In addition to studying the
phenomenology of linear and quadratic interactions separately, we examine their
interplay. We review the different experiments that can probe such interactions
and present the current and expected future bounds on the parameter space. In
particular, we discuss the scalar field solution presented in [A. Hees, O.
Minazzoli, E. Savalle, Y. V. Stadnik and P. Wolf, Phys.Rev.D 98 (2018) 6,
064051], and extend it to theories that capture both the linear and the
quadratic couplings of the DM field to the SM. Furthermore, we discuss the
theoretical aspects and the corresponding challenges for natural models in
which the quadratic interactions are of phenomenological importance.
