Serious searches for the weakly interacting massive particle (WIMP) have now begun. In this context, the most important questions that need to be addressed are: To what extent can we constrain the WIMP models in near future? and What will then be the remaining unexplored region in the WIMP parameter space for each model? In our quest to answer these questions, we classify WIMP in terms of quantum number and study each case adopting minimality as a guiding principle. We first study one of the simple cases of the minimal composition in the well-tempered fermionic WIMP regime, namely the singlet-doublets WIMP model. Next, we consider the non-well-tempered fermionic WIMP regime where the WIMP is almost described by a SU(2)L gauge eigenstate. We first study the WIMP whose weakcharge is almost one as the minimal case, namely the SU(2)L-triplet WIMP model. After that, we discuss the other models where WIMP carries no weakcharge, namely (almost) the standard model (SM) singlet WIMP.