The Cosmological Constant(CC) Problem emerges in Quantum Field Theory (QFT) in curved space-time due to the enormous magnitude of the induces vacuum energy. After reviewing the CC problem we consider the possibility of a variable CC due to the quantum effects of matter fields. Assuming the standard (Appelquist and Carazzone) form of decoupling of massive fields at low energies we arrive at the cosmological models with the potentially observable predictions. These cosmological models have strong relation to quantum field theory, particle physics and manifest many interesting features.