The Galactic Centre region is noteworthy for its massive black hole, bursts of star formation, network of highly magnetised filaments, and bipolar outflow to the halo. This region is of high interest to characterise the nuclei of spiral galaxies and the interstellar medium in starburst galaxies, but its study is hampered by confusion with Galactic activity along the 8.15 kpc-long sightlines to the centre. I will review the series of extraplanar lobes, chimneys, and bubbles seen from the radio to the gamma rays. They highlight the intense activity of the region over the past few million years, but we do not know their spatial relation to the centre and to each other, and their spectral properties are often biased by foreground absorption or contamination. In gamma rays, the Fermi Bubbles and an excess of GeV emission towards the centre could shed important light on past eruptions from Sgr A*, on the launch of the Galactic wind, on cosmic-ray production and transport in the starburst nucleus, and on the dynamical history of millisecond pulsars in the bulge. Determining the spatial and spectral distribution of the base of the Fermi Bubbles and of the central GeV excess is, however, extremely challenging because of the unknown distribution of the intense foreground emission. I will discuss the systematic biases that currently limit the characterisation of these important features, thereby limiting tests of their origin, as well as a conclusive assessment of the potential level of dark-matter annihilation.