Problems of quantum field theory with unstable vacuum are considered. In the case of quantum electrodynamics, the vacuum unstability is connected with the possibility of pair creating by external electromagnetic fields already in zeroth order with respect to the radiation interaction. The perturbation theory is constructed, for which the interaction with the external field is kept exact. Exact Green functions are introduced and the functional formulation is discussed. Perturbation theory for calculating the mean values of the Heisenberg operators and the total probabilities of radiating processes is built in the case under consideration. All results referring to the relations of the optical theorem for the external fields with unstable vacuum are presented. All these particularities are demonstrated for concrete external fields. Problems of the quantum electrodynamics at finite temperature are considered.