The photon-ion merged-beams technique for the photoionisation of mass/charge selected ionised atoms, molecules and clusters by x-rays from synchrotron radiation sources is introduced. Examples for photoionisation of atomic ions are discussed by going from outer shell ionisation of simple few electron systems to inner shell ionisation of complex many electron ions. Fundamental ionisation mechanisms are elucidated and the importance of the results for applications in astrophysics and plasma physics is pointed out. Finally, the unique capabilities of the photon-ion merged-beams technique for the study of photoabsorption by nanoparticles are demonstrated by the example of endohedral fullerene ions.