In molecular crystals a charge carrier and a molecular (Frenkel) exciton are attracted to each other. This attraction arises from the increase of the molecular static polarizability upon electronic excitation, and may be responsible for the formation of a two-particle bound state of the exciton and the free charge. Such charged Frenkel excitons are analogous to trions (bound states of a Wannier-Mott exciton and a charge carrier) in inorganic semiconductors. In this paper we develop a theory of charged excitons in molecular crystals, and apply this theory to study the spectra of charged Frenkel excitons in two-dimensional structures, which serve as a rather good approximation for layered crystals like anthracene, tetracene. We show that the binding energy of charged Frenkel excitons can be of the order of several hundred cm-1. Thus, they may be stable at room temperatures, in contrast to trions in inorganic semiconductors. Particularly interesting is the possibility of forming charged triplet excitons in the crystal of tetracene where the energy of the lowest triplet exciton is much smaller than the energy of the lowest excitation in ions. This circumstance prevents the transformation of charged triplet excitons into an ion excitation with short lifetime and promotes the formation of rather stable charged triplet excitation. We briefly discuss the optical properties of charged Frenkel excitons and the effects of a static electric field.