The Borexino experiment is operational at Laboratori Nazionali del Gran Sasso since 2007. Its technical distinctive feature is the unprecedented ultralow background of the inner scintillating core, which is the basis of the outstanding achievements obtained by the experiment. After recalling the main features of the detector, we review the solar and geoneutrino results accumulated so far, with special emphasis to the most recent and prominent results. Specifically, these are on the one hand the measure of the fundamental pp solar neutrino flux, which is the direct probe of the engine mechanism powering our star, and on the other the detection of the geo-neutrino signal with its geophysical implications for the interior of the Earth. The pp-neutrino milestone measurement puts Borexino in the unique situation of being the only experiment able to do solar neutrino spectroscopy over the entire solar spectrum; the counterpart of this peculiar status in the oscillation interpretation of the data is the capability of Borexino alone to perform the full validation across the solar energy range of the MSW-LMA paradigm. We conclude highlighting the plans to fully complete the solar spectroscopy with the missing piece of the CNO neutrinos. If successful, such a measurement would represent the final crowning of the long quest of Borexino to unravel all the properties of the neutrinos from the Sun.