When in October 1957 the first artificial satellite, Sputnik 1, was launched by the USSR, nobody could imagine that after less than 50 years we would be facing an environmental problem in the near- Earth space. A few years later, on 29 June 196l anotherkey event happened, even if less resoundingfrom the political and scientific point of view, that should have raised some concern.The first known break-up in orbit, the explosion of the Transit 4A rocket body took place. From then on, the repetition of thesetwo events(launches of new satellites and break-up of in orbit spacecraft) contributed to build up a huge population of objects that are now polluting, perhaps irreversibly, space around us. Many yearslater,on24 July 1996, the the danger posed by the space debris to all the human activities in space has been clearly showed by the first recorded accidental collision between an operational satellite and a piece of debris: the French micro-satellite Cerise has been hit, at the relative velocity of 14.77km/s, by a fragment, of about l0 cm2, coming from the explosion of an Ariane rocket upper stage,that had happened years before In near-Earth space there are two major regions where orbital debris is of concern:Low Earth Orbits (LEOs),below about 2,000km, and Geosynchronous Orbits (GEOs),at an altitude of about 36,000km. The issuesare in principle, the same in the two regions. Nevertheless, they require different approaches and solutions.In this paper, we will describe the present situation and the future evolution of the space debris environment in Earth orbit, with a particular focus on LEOs, where the situation appears be deteriorating rapidly