The discovery of fullerenes in 1985 opened up a new, unexpected world of exciting carbon nanostructures. I will give a brief overview of the developments in the field since then and show how carbon nanotubes have become one of the hottest topics in physics today. Their spectacular mechanical properties combined with extremely high thermal conductivity and interesting electronic properties make carbon nanotubes interesting for a wide range of potential applications. Already their mechanical properties are being exploited in composite materials and considerable progress is being made towards integrating carbon nanotubes into silicon electronics. I will discuss some of the work being done in Göteborg concerning the growth and characterization of nanotubes and the fabrication of electronic and nanoelectromechanical devices.