Because the Earth’s atmosphere is not transparent for the most of the electromagnetic waves, Space Astronomy was born in 1960s to complement ground-based observations and to provide us with multiwavelength data from gamma-ray to radio. Most Space observatories work in gamma-ray, X-ray, UV and IR, as well as there are also optical and other Space telescopes. We will review the most important Space telescopes: their important technical parameters, scientific results and discoveries. Among them there are (by increasing wavelengths) Fermi, Swift, INTEGRAL, ROSAT, Chandra, XMM, GALEX, Hubble, Gaia, James Webb, Herschel, WISE, Spitzer, IRAS and many others. These telescopes make the Space Astronomy truly multiwavelength and the combination with ground-based data allows us to have better understanding of the Universe and phenomena going on in its all varieties.