The D.O.R.T. method (Decomposition de l'Operateur de Retournement Temporel) generalizes the principle of acoustic time reversal mirrors. It applies to detection and focusing with large arrays of transducers [Prada et al., J. Acoust. Soc. Am. 99 (1996)]. A transducer array insonifying a scattering medium is characterized by its frequency-dependent transfer matrix K((omega)). The time-reversal process is then described by time-reversal operator K((omega))K[sup *]((omega)). The eigenvalue decomposition of this hermitian operator provides a classification and a localization of the scattering centers in the medium. The two main steps of the D.O.R.T. method are the measurement of the interelement impulse responses of each pair of elements in the array and the diagonalization of the corresponding time reversal operator at chosen frequencies. The method is efficient for the detection and selective focusing in an inhomogeneous multiple target medium. It also applies to the recognition of shells, in particular to the detection and characterization of circumferential waves propagating around the shell. The D.O.R.T. method and recent experiments of detection through channels and through inhomogeneous media will be presented.