  We review the properties of nonlinear, multidimensional localized waves whose
stationary propagation is sustained by a dynamic equilibrium between
self-focusing and nonlinear losses. Their finite-energy versions preserve light
bullet behavior well-beyond the characteristic diffraction or dispersion
distances, and rebuild after obstacles. There exists a preferential lossy light
bullet with maximum intensity and losses, defined solely by the optical
properties of the medium, which is the most stable, non-conical localized wave
supported by a medium with self-focusing nonlinearity and nonlinear losses.
This preferential lossy light bullet acts as an attractor during self-focusing
of Gaussian-like wave packets when collapse is halted by nonlinear absorption,
a fact that can explain relevant characteristics of the observed light filament
dynamics in media with anomalous dispersion.
