The resonance phenomenon is a fundamental subject in nuclear physics and in reactor physics. This chapter explains how resonances affect the probability that a neutron will be slowed down to thermal energy, known as resonance escape probability. The cases of an homogeneous and an heterogeneous medium are presented. An heterogeneous geometry also produces an effect called spatial self shileding, which improves the resonance escape probability. The last part of this chapter introduces the phenomenon of Doppler broadening, which constitutes a temperature effect and is of major importance for the Safety of reactors.