The classification of universal amplifiers presented in this paper places all operational amplifiers and current conveyors known from the literature into a common framework, together with abstract concepts such as the universal active element and the nullor. Our approach is new in that we base it on four-terminal theory, which results in a classification that is more extensive but not more complex than classifications derived using two-port theory. It turns out that our classification contains a new type of operational amplifier, which we call current-feedback operational transconductance amplifier (CFB OTA), and also a new class of voltage-inverting current conveyors. We then demonstrate that our classification is very closely related to integrated-amplifier design by showing how all operational amplifiers and current conveyors can be implemented in CMOS using only a few CMOS circuits. Since the basic ideas behind CMOS and bipolar circuits are very similar, this paper is not process specific and can be seen as an attempt to bridge the gap between amplifier theory and amplifier design that has become ever wider in the past few years.