The problem of particle interferometry in weak inertial or gravitational fields is treated from a unified point of view. The effect of the fields can be confined to a phase factor to be determined by quadratures once the solution of the possibly non-linear wave equation describing the particles is known. The procedure is completely Lorentz invariant and gauge invariant, can be extended to higher orders and applies to a wide range of interferometers, from optical ones to those using superfluids. Results already reported in the literature are re-obtained and in some cases improved. Other results known to hold for stationary fields are extended to time-dependent fields. It is also shown that interferometers hold promise as broad-band detectors of gravitational radiation even at high frequencies.