This paper introduces memristor-based operational amplifiers (OpAmps) in which semiconductor resistors are suppressed and replaced by memristors. The ability of the memristive elements to hold several resistance states is exploited to design programmable closed-loop OpAmps. An inverting OpAmp, an integrator and a differentiator are studied. Such designs are developed based on a calibrated memristor model, and offer dynamic configurability to realize different gains and corner frequencies at reduced chip area.