We describe theoretically novel excitons in self-assembled quantum dots interacting with a two-dimensional (2D) electron gas in the wetting layer. In the presence of the Fermi sea, the optical lines become strongly voltage-dependent. If the electron spin is nonzero, the width of optical lines is given by kBTK, where TK is Kondo temperature. If the spin is zero, the exciton couples with the continuum due to Auger-like processes. This leads to anticrossings in a magnetic field. Such states can be called Kondo-Anderson excitons. Some of the described phenomena are observed in recent experiments.