Asteroid and lunar mining has been an SF staple since the 1950s; see for instance The Rolling Stones , a 60 years old YA novel by Robert Heinlein, or the Belter profession in the 1970s role-playing game Traveller. Space technology has developed rapidly during recent years and now people have started looking into real-world versions of such enterprises.
Extraterrestrial mining would of course be very expensive, but there are a few metals so precious that it would justify the cost. However, the legal status of resources found beyond Earth is not crystal clear. It is a matter of how to interpret the international treaties regulating the solar system. The venture capitalists looking at the asteroid belt would now like to know how such businesses are to be regulated — link for more on the subject >>>