RR Lyrae stars have long been popular standard candles, but significant advances in methodology and technology have been made in recent years to increase their precision as distance indicators. We present multi-wavelength (optical UBVRcIc and Gaia G,BP,RP; near-infrared JHKs; mid-infrared [3.6],[4.5]) period-luminosity-metallicity (PLZ), period-Wesenheit-metallicity (PWZ) relations, calibrated using photometry obtained from The Carnegie RR Lyrae Program and parallaxes from the Gaia second data release for 55 Galactic field RR Lyrae stars. The metallicity slope, which has long been predicted by theoretical relations, can now be measured in all passbands. The scatter in the PLZ relations is on the order of 0.2 mag, and is still dominated by uncertainties in the parallaxes. As a consistency check of our PLZ relations, we also measure the distance modulus to the globular cluster M4, the Large Magellanic Cloud (LMC) and the Small Magellanic Cloud (SMC), and our results are in excellent agreement with estimates from previous studies.