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tokens: Our images also show that the extended Ly emission is typically quite symmetric (albeit with interesting deviations in some objects) – information which is necessarily erased in any stacking process. It will be intriguing to compare the Ly halo maps obtained by MUSE with simulated views from (possibly competing) model predictions. In the context of our simple phenomenological model, two main parameters govern the overall appearance of a Ly halo at : the halo scale length, typically 10 times larger than the scale length of the central continuum source, and the fraction of the total Ly radiation emitted by the halo, typically between 40% and 90%. These two quantities are essentially uncorrelated in our sample, which may indicate that they are physically determined at different scales. The size of a halo would then mainly depend on the spatial distribution and kinematic structure of the circumgalactic gas, independently of how much Ly it emits. On the other hand, the halo luminosity fraction will depend on the origin of the Ly radiation, but also on the importance of resonant scattering of Ly photons from inside the galaxy into the halo. Energetically, our measurements are consistent with the idea that most of the observed Ly radiation is produced within the UV-bright star-forming regions of the galaxies and then scattered outwards. However, additional processes for powering the Ly emission in the extended haloes are not excluded, and more theoretical and modelling work will be required to explore the relative importance of different mechanisms. Additional clues will come from spatially resolved spectroscopy of Ly haloes, which MUSE will enable us to perform at least for the brighter sources (or in strongly lensed objects where the magnification helps to reach even higher spatial resolution; see Patrício et al. 2016 for a first case study using MUSE). By a remarkable coincidence, individual Ly haloes of nearby () galaxies have just now become a subject of detailed scrutiny through the LARS project ( Hayes et al. 2013 ; Östlin et al. 2014 ; Hayes et al. 2014 ; Guaita et al. 2015 ). While the LARS galaxies can be resolved in much greater detail than our faint HDFS sources, the overall comparison of high- and low-redshift Ly halo properties shows some similarities, but also intriguing differences. In particular, the huge discrepancy between the sizes of Ly-emitting regions around and galaxies (Fig. 12 ) suggests that the nature of the circumgalactic medium has changed drastically from the epoch of galaxy formation to the present-day Universe. For the first time, MUSE has allowed us to assess the level of diversity in the Ly halo properties of high-redshift galaxies. While admittedly our sample is too small to go very far in this direction, much more can be expected in the future, as MUSE has just commenced operation. Furthermore, the MUSE data need to be complemented by observations with other instruments and in other wavelengths. In this respect