  We enumerate the set of simplified models which match onto the complete set
of gauge invariant effective operators up to dimension six describing
interactions of a singlet-like Majorana fermion dark matter with the standard
model. Tree level matching conditions for each case are worked out in the large
mediator mass limit, defining a one to one correspondence between the effective
operator coefficients and the simplified model parameters for weakly
interacting models. Utilizing such a mapping, we compute the dark matter
annihilation rate in the early universe, as well as other low-energy
observables like nuclear recoil rates using the effective operators, while the
simplified models are used to compute the dark matter production rates at high
energy colliders like LEP, LHC and future lepton colliders. Combining all
relevant constraints with a profile likelihood analysis, we then discuss the
currently allowed parameter regions and prospects for future searches in terms
of the effective operator parameters, reducing the model dependence to a
minimal level. In the parameter region where such a model-independent analysis
is applicable, and leaving aside the special dark matter mass regions where the
annihilation proceeds through an s-channel Z or Higgs boson pole, the current
constraints allow effective operator suppression scales ($\Lambda$) of the
order of a few hundred GeV for dark matter masses $m_\chi >$ 20 GeV at $95\%$
C.L., while the maximum allowed scale is around $3$ TeV for $m_\chi \sim
\mathcal{O}(1\,{\rm TeV})$. An estimate of the future reach of ton-scale direct
detection experiments and planned electron-positron colliders show that most of
the remaining regions can be probed, apart from dark matter masses near half of
the Z-boson mass (with $500\,{\rm GeV} < \Lambda < 2\,{\rm TeV} $) and those
beyond the kinematic reach of the future lepton colliders.
