The risk of humanity extinction by giant asteroid impact is addressed. A 100 km sized asteroid impact may transform the Earth into an inhospitable planet, thus causing the extinction of many life forms including the human species. The exact reason for such a result remains nevertheless uncertain. Based on Moon crater history and NEA observations, the probability of a giant impact is between 0.03 and 0.3 for the next billion years. However, as the warning time would be in general relatively long, humanity could have time to settle on other planets with a high probability of success. The greatest threat could come from giant long period comets. We show that the probability of a giant comet impact is 2.2 × 10-12 for the next hundred years with a very short warning time. Many possible causes would lead to a degradation of life support and the extinction of humanity during the decades following the impact. It could be a lack of energy or important resources, other catastrophic events, conflicts and inefficient human organization and the preparatory phase could also play an important role. All in all, the extinction would be highly probable though not totally sure.