We have started a study of quantum ferroelectrics and paraelectrics. Simple two-dimensional short-range lattice model Hamiltonians are constructed, keeping in mind the phenomenology of real perovskite systems, like ${\mathrm{SrTiO}}_{3}$ and ${\mathrm{KTaO}}_{3}$. Pertinent quantum tunneling phenomena, and the presence of an icelike constraint are demonstrated. The two simplest models, namely a plain quantum four-state clock model and a constrained one, are then studied in some detail. We show the equivalence of the former, but not of the latter, to a quantum Ising model. For the latter, we describe a very good analytical wave function valid in the special case of zero coupling (J=0). In order to study the full quantum statistical mechanics of these models, a path-integral Monte Carlo calculation is set up, and implemented with a technique, which even in the constrained case permits a good convergence for increasing time slice number m. The method is applied first to the unconstrained model, which serves as a check, and successively to the constrained quantum four-state clock model. It is found that in both cases a quantum phase transition at T=0 takes place at finite coupling J, between a ferroelectric and a quantum paraelectric state, even when the constraint hinders disordering of the ferroelectric state. These model paraelectric states have a finite excitation gap, and no broken symmetry. The possible role of additional (``oxygen hopping'') kinetic terms in making closer contact with the known phenomenology of ${\mathrm{SrTiO}}_{3}$is proposed.