  We describe the evolution of Dark Matter (DM) abundance from the very onset
of its creation from inflaton decay under the assumption of an instantaneous
reheating. Based on the initial conditions such as the inflaton mass and its
decay branching ratio to DM, reheating temperature, and the DM mass and
interaction rate with the thermal bath, the DM particles can either thermalize
(fully/partially) with the primordial bath or remain non-thermal throughout
their evolution history. In the thermal case, the final abundance is set by the
standard freeze-out mechanism for large annihilation rates, irrespective of the
initial conditions. For smaller annihilation rates, it can be set by the
freeze-in mechanism, also independent of the initial abundance, provided it is
small to begin with. For even smaller interaction rates, the DM decouples while
being non-thermal, and the relic abundance will be essentially set by the
initial conditions. We put model-independent constraints on the DM mass and
annihilation rate from over-abundance by exactly solving the relevant Boltzmann
equations, and identify the thermal freeze-out, freeze-in and non-thermal
regions of the allowed parameter space. We highlight a generic fact that
inflaton decay to DM inevitably leads to an overclosure of the Universe for a
large range of DM parameter space, and thus poses a stringent constraint that
must be taken into account while constructing models of DM. For the thermal DM
region, we also show the complementary constraints from indirect DM search
experiments, Big Bang Nucleosynthesis, Cosmic Microwave Background, Planck
measurements, and theoretical limits due to the unitarity of S-matrix. For the
non-thermal DM scenario, we show the allowed parameter space in terms of the
inflaton and DM masses for a given reheating temperature, and compute the
comoving free-streaming length to identify the hot, warm and cold DM regimes.
