Carbon nanotubes and, more recently, semiconducting nanowires are attracting considerable interest as building blocks for a wide variety of nanodevices. Many relevant proofs of concept have already been provided such as field effect transistors, elementary logic circuits, light emitting diodes, lasers, and biochemical sensors. At the same time, the increasing quality of these nanostructures is opening new possibilities for low-temperature applications and for the study of fundamental quantum phenomena. In this talk I will present the results of mesoscopic transport experiments with individual III-V nanowires and single-walled carbon nanotubes. In particular I will report on 1) the observation of a tunable Josephson supercurrent in InAs nanowires contacted by superconducting electrodes, and 2) the observation of orbital Kondo physics in carbon nanotube quantum dots.