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A theory of analog resonances is reviewed which makes use of projection operators. The Hilbert space is divided into three parts: a continuum or open-channel space, an analog-state space, and a compound space. The phenomena are discussed in terms of the dynamical coupling of these spaces. The parameterization of the $T$ matrix is discussed in detail, and equations are presented for various cross sections. The commutator [$H$, ${T}_{\ensuremath{-}}$], where ${T}_{\ensuremath{-}}$ is the isospin-lowering operator, plays an important role in the theory, and the various terms which contribute to this commutator are discussed. The energy splitting of the isospin multiplet, i.e., the Coulomb displacement energy, is discussed in detail. The importance of the analog resonance phenomena for the extraction of spectroscopic information is stressed, and it is shown how such information may be obtained. Various processes which contribute to the escape amplitude of the analog state are classified, and some numerical estimates are given. For several regions of the Periodic Table, graphs are presented for the various theoretical escape amplitudes, continuum energy shifts, asymmetry phases, and optical phase shifts, etc. Spectroscopic factors are calculated and compared with those obtained in other experiments.