The Gaia-ESO survey (GES) is now in its fifth and last year of observations, and has already produced tens of thousands of high-quality spectra of stars in all Milky Way components. This paper presents the strategy behind the selection of astrophysical calibration targets, ensuring that all GES results on radial velocities, atmospheric parameters, and chemical abundance ratios will be both internally consistent and easily comparable with other literature results, especially from other large spectroscopic surveys and from Gaia. The calibration of GES is particularly delicate because of: (i) the large space of parameters covered by its targets, ranging from dwarfs to giants, from O to M stars, and with a large range of metallicities, as well as including fast rotators, emission line objects, stars affected by veiling and so on; (ii) the variety of observing setups, with different wavelength ranges and resolution; and (iii) the choice of analyzing the data with many different state-of-the art methods, each stronger in a different region of the parameter space, which ensures a better understanding of systematic uncertainties. An overview of the GES calibration and homogenization strategy is also given, along with some examples of the usage and results of calibrators in GES iDR4 - the fourth internal GES data release, that will form the basis of the next GES public data release. The agreement between GES iDR4 recommended values and reference values for the calibrating objects are very satisfactory. The average offsets and spreads are generally compatible with the GES measurement errors, which in iDR4 data already meet the requirements set by the main GES scientific goals.