A review is first given of presently available techniques for generating and observing long-lived dianions of molecules and of clusters in the gas phase. Multiply charged anions that have been unambiguously observed are listed with the technique used to detect them. The remainder of the article is then devoted to the way quantum chemistry can contribute to the continuing search for multiply charged negative ions. This discussion is divided into two parts : (i) ions in zero magnetic fields and (ii) ions in intense magnetic fields. In (i) it is difficult to bind even two electrons to a heavy neutral atom. In (ii), however, a heavy atom with atomic number Z can bind an additional Z electrons, the binding energy of these additional electrons being on the same order as that of the first Z electrons, in the so-called "hyperstrong" field regime. Diatomic homonuclear molecules have binding energies on the order of the separated atom energies. As there should be precursor effects, it is proposed that one should attempt multiply-charged anion formation in the highest available magnetic fields in the laboratory.