We present the Red Unknowns: Bright Infrared Extragalactic Survey (RUBIES) providing JWST/NIRSpec spectroscopy of red sources selected across ∼150 arcmin2 from public JWST/NIRCam imaging in the UDS and EGS fields. The novel observing strategy of RUBIES offers a well-quantified selection function. The survey has been optimised to reach high (>70%) spectroscopic completeness for bright and red (F150W-F444W>2) sources that are very rare. To place these rare sources in context, we simultaneously observed a reference sample of the 23 using only the G395M disperser. The RUBIES data reveal a highly diverse population of red sources that span a broad redshift range (zspec∼1-9), with photometric redshift scatter and an outlier fraction that are three times higher than for similarly bright sources that are less red. This diversity is not apparent from the photometric spectral energy distributions (SEDs). Only spectroscopy reveals that the SEDs encompass a mixture of galaxies with dust-obscured star formation, extreme line emission, a lack of star formation indicating early quenching, and luminous active galactic nuclei. As a first demonstration of our broader selection function we compared the stellar masses and rest-frame U-V colours of the red sources and our reference sample. We find that the red sources are typically more massive (M∗∼1010-11.5 M⊙) across all redshifts. However, we also find that the most massive systems span a wide range in U-V colour. We describe our data reduction procedure and data quality, and we publicly release the reduced RUBIES data and vetted spectroscopic redshifts of the first half of the survey through the DAWN JWST Archive.