A method of combating bed bugs and/or other insects in a locus containing or susceptible to presence of same, in which a DMSO-containing formulation is applied to the locus. Various pesticidal compositions are disclosed as useful for such purpose, including compositions in which DMSO is in combination with an alcohol and/or another pesticidal active agent. Compositions of the disclosure can be applied to a variety of loci, to effectively eradicate bed bugs for extended periods of time.