  In conventional lasers, the optical cavity that confines the photons also
determines essential characteristics of the lasing modes such as wavelength,
emission pattern, ... In random lasers, which do not have mirrors or a
well-defined cavity, light is confined within the gain medium by means of
multiple scattering. The sharp peaks in the emission spectra of semiconductor
powders, first observed in 1999, has therefore lead to an intense debate about
the nature of the lasing modes in these so-called lasers with resonant
feedback. In this paper, we review numerical and theoretical studies aimed at
clarifying the nature of the lasing modes in disordered scattering systems with
gain. We will discuss in particular the link between random laser modes near
threshold (TLM) and the resonances or quasi-bound (QB) states of the passive
system without gain. For random lasers in the localized regime, QB states and
threshold lasing modes were found to be nearly identical within the scattering
medium. These studies were later extended to the case of more lossy systems
such as random systems in the diffusive regime where differences between
quasi-bound states and lasing modes were measured. Very recently, a theory able
to treat lasers with arbitrarily complex and open cavities such as random
lasers established that the TLM are better described in terms of the so-called
constant-flux states.
