We study theoretically the interaction of a polyampholyte chain with charged planes, cylinders, and spheres. Due to the random character of the charge distribution along the chain, a polyampholyte possesses a spontaneous dipole moment, which can interact favorably with charged objects. Depending on the charge strength of the object and the polyampholyte length and fraction of charged monomers, this attractive interaction can be strong enough to induce adsorption. The addition of salt weakens the trend to adsorption, but proves necessary to adsorb polyampholytes of the same net charge as the charged object in the case of planes and cylinders. Long polyampholytes form globules, for which the number of uncompensated charges and thus the spontaneous dipole moment is reduced. Nevertheless, globules can adsorb on charged objects via two pathways : they either adsorb as a whole, (intact globule), or they are dissolved into a coil state prior to adsorption. Applications to the complexation behavior of polyampholytes with stiff, rodlike polyelectrolytes and with charged microspheres or charged spherical micelles are given.