The steadily growing interest to parity-time (PT-) symmetric systems has started out in non-Hermitian quantum mechanics, where complex potentials obeying PT symmetry can exhibit all-real spectra. Driven by the mathematical similarity between the quantum mechanical Schroedinger equation and dispersive wave models, the concept of PT symmetry later spread out to optics, Bose-Einstein condensates, and many other physical fields where the description of nonlinear effects is of profound importa​nce. PT-symmetric systems are characterized by a judicious balance between gain and loss. In optics, it can be implemented by a properly designed profile of the complex-valued refractive index. In an atomic condensate, PT symmetry corresponds to the situation where particles are injected into the system at some spot and are simultaneously eliminated from the condensate at a different spot, with the gain and loss rates being equal. Therefore, from the dynamical point of view, PT-symmetric systems are inherently open and dissipative. At the same time, PT symmetry gives rise to a wide array of new phenomena which have no counterparts in traditional dissipative systems. In our talk we will discuss one of these unusual features which is the existence of continuous families of PT-symmetric solitons (in contrast to traditional systems with gain and loss where dissipative solitons appear as isolated attractors). Moreover, we will demonstrate that there exists another class of generically asymmetric complex potentials which enjoy the same unusual property.