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Context. XMM-Newton was launched on 10 December 1999 and has been operational since early 2000. One of the instruments onboard XMM-Newton is the reflection grating spectrometer (RGS). Two identical RGS instruments are available, with each RGS combining a reflection grating assembly and a camera with charge-coupled devices to record the spectra. Aims. We describe the calibration and in-orbit performance of the RGS instrument. By combining the preflight calibration with appropriate inflight calibration data including the changes in detector performance over time, we aim at profound knowledge about the accuracy in the calibration. This will be crucial for any correct scientific interpretation of spectral features for a wide variety of objects. Methods. Ground calibrations alone are not able to fully characterize the instrument. Dedicated inflight measurements and constant monitoring are essential for a full understanding of the instrument and the variations of the instrument response over time. Physical models of the instrument are tuned to agree with calibration measurements and are the basis from which the actual instrument response can be interpolated over the full parameter space. Results. Uncertainties in the instrument response have been reduced to <10% for the effective area and <6 mÅ for the wavelength scale (in the range from 8 Å to 34 Å). The remaining systematic uncertainty in the detection of weak absorption features has been estimated to be 1.5%. Conclusions. Based on a large set of inflight calibration data and comparison with other instruments onboard XMM-Newton, the calibration accuracy of the RGS instrument has been improved considerably over the preflight calibrations. [ABSTRACT FROM AUTHOR]