A semiclassical double-well model of dielectric relaxation current in glasses is extended to (i) nonzero temperature, (ii) complex bias histories, and (iii) strong electric fields. At finite temperature, thermal excitation yields a contribution linear in temperature, which adds to the temperature-independent contribution from tunneling from the zero-temperature case. Both contributions vary linearly with applied field and have a time dependence of 1/tn. Experimental measurements in three different glasses are shown to agree with this prediction, and it is shown how to use such measurements to estimate the material parameters t0 and σ0. For complex bias histories, a principle of superposition is found, as observed experimentally, if the applied fields are weak compared to the material parameter E0, estimated to be on the order of 107 V/m. For an electric field pulsed periodically from 0 to E, the current can be decomposed into a fast contribution due to particles tunneling back and forth every cycle of the field, and a slow residual contribution whose time dependence is the same as that for a continuous bias, but whose magnitude is reduced by the duty cycle of the periodic bias. For a sinusoidal electric field, thermal excitation gives a contribution to the dielectric constant that varies linearly with temperature and has a real part that varies logarithmically with frequency and an imaginary part that varies as the inverse tangent of frequency. For tunneling, both parts are independent of temperature and vary approximately as the logarithm of frequency, a dependence observed experimentally and almost indistinguishable from that suggested by the 1/tn current response to a step voltage. For strong electric fields, the current that flows after the field is removed is found to be dominated by particles that fell forward when the field was on. Since particles fall forward quickly but tunnel back slowly, even strong fields applied for a short period of time can produce a large, long-lasting return current. These analyses lead to a number of testable predictions, and should be useful for understanding the phenomenon of dielectric relaxation and its impact on electronic devices.