A great many results have been obtained by INAF researchers in diverse fields within astronomy and astrophysics, and using various instruments. For example, the all Italian satellite, AGILE, that through its Italian leader has led to important results on the high energy Universe and the study of black holes (like Cygnus X-3). Amongst AGILE's discoveries, also the fact that our own atmosphere, under certain conditions (super-cell tropical thunder storms), can produce phenomena such as terrestrial gamma-ray bursts. "Lightning" of such high energy as to render the Faraday cage which protects aeroplanes from normal lightning insufficient. For this reason INAF and ASI are in contact with ENAC to look into this potentially destructive phenomenon. Here we have then, a satellite designed to study the Universe, that makes a discovery concerning our own home planet. Amongst the international collaborations that INAF can claim, one of the most important is related to the LBT (Large Binocular Telescope), the largest of its type, and amongst the most advanced in the world. Thanks to it's new adaptive optics system, developed by researchers at INAF's Arcetri Observatory, the LBT has been able, at optical wavelengths, to exceed the image sharpness of the Hubble Space Telescope, a milestone in observations of the Universe and something considered impossible until recently for a ground based telescope. VIMS and VIRTIS are two instruments designed and built by INAF; the first operates on the Cassini probe that has been revealing the mysteries of Saturn and its moons since 2004. VIRTIS is busy on ESA's Venus Express probe, designed particularly to study the greenhouse effect on this planet, something that is fundamental for our understanding of how climate change and non-reversible effects could result from careless behaviour on our own planet. ESA's Planck satellite, thanks to its LFI instrument built by a team of researchers coordinated by INAF, has made the best map ever of the cosmic background radiation, emitted 13.7 billion years ago. This is a critical step in understanding how the Universe formed and is evolving. INAF doesn't work only on data from its own instruments, but also on those of others, such as the telescopes of ESO, a European organisation of which Italy is a member. Thanks to these telescopes, our researchers have discovered that Mercury shows signs of recent volcanic activity and that galaxies grow not only by merging with each other but also by swallowing hydrogen. One could continue with the discoveries made on supernovae, pulsars and black holes, on gamma ray bursts and extra-solar planets, on the cosmic background radiation and the evolution of the Universe.