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Context. The Gaia-ESO Survey (GES) is a public, high-resolution spectroscopic survey, conducted with the multi-object spectrograph Fibre Large Array Multi Element Spectrograph (FLAMES) on the Very Large Telescope (European Southern Observatory, ESO, Cerro Paranal, Chile) from December 2011 to January 2018. Gaia-ESO has targeted all the main stellar components of the Milky Way, including thin and thick disc, bulge, and halo. In particular, a large sample of open clusters has been observed, from very young ones, just out of the embedded phase, to very old ones. Aims. The different kinds of clusters and stars targeted in them are useful to reach the main science goals of the open cluster part of GES, which are the study of the open cluster structure and dynamics, the use of open clusters to constrain and improve stellar evolution models, and the definition of Galactic disc properties (e.g., metallicity distribution). Methods. The Gaia-ESO Survey is organised in 19 working groups (WGs), each one being responsible for a task. We describe here the work of three of them, one in charge of the selection of the targets within each cluster or association (WG4), one responsible for defining the most probable candidate member stars (WG1), and another one in charge of the preparation of the observations (WG6). As the entire GES has been conducted before the second Gaia data release, we could not make use of the Gaia astrometry to define cluster member candidates. We made use of public and private photometry to select the stars to be observed with FLAMES, once brought on a common astrometric system (the one defined by 2MASS). Candidate target selection was based on ground-based proper motions, radial velocities, and X-ray properties when appropriate, for example, and it was mostly used to define the position of the clusters' evolutionary sequences in the colour-magnitude diagrams. Targets for GIRAFFE were then selected near the sequences in an unbiased way. We used known information on membership, when available, only for the few stars to be observed with UVES. Results. We collected spectra for 62 confirmed clusters in the main observing campaign (and a few more clusters were taken from the ESO archive). Among them are very young clusters, where the main targets are pre-main sequence stars, clusters with very hot and massive stars currently on the main sequence, intermediate-age and old clusters where evolved stars are the main targets. Our strategy of making the selection of targets as inclusive and unbiased as possible and of observing a significant and representative fraction of all possible targets permitted us to collect the largest, most accurate, and most homogeneous spectroscopic data set on open star clusters ever achieved. [ABSTRACT FROM AUTHOR]