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We show that a common language can be used to unify the description of parametrically coupled circuits—parametric amplifiers, frequency converters, and parametric nonreciprocal devices—with that of band-pass filter and impedance matching networks. This enables one to readily adapt network synthesis methods from microwave engineering in the design of parametrically coupled devices having prescribed transfer characteristics, eg, gain, bandwidth, return loss, and isolation. We review basic practical aspects of coupled-mode theory and filter synthesis, and then show how to apply both, on an equal footing, to the design of multipole, broadband parametric and nonreciprocal networks. We supplement the discussion with a range of examples and reference designs.