Resolving neutron stars physics and geometry

The unprecedented harvest of X-ray photons detected from dozens of isolated neutron stars has made it possible to glimpse at their emission mechanisms as well as at their emission geometry. Rotating hot spot(s), superimposed to the global thermal emission from the neutron star surface, are seen from several objects, allowing to probe the stars' external heating sources. Non-thermal emission is also seen to vary as the stars rotate. Moreover, absorption features have been detected in the spectra of several objects, allowing to probe (tentatively) the stars' magnetic fields. Spectacular tails, trailing the stars' supersonic motion, trace the boundaries of the relativist winds streaming from the star's magnetosphere. Apart from classical radio pulsar and certified radio-quiet neutron stars, XMM-Newton has devoted significant observation time to the enigmatic central compact objects, presumably isolated neutron stars shining at the center of their supernova remnants. Far from showing a unifying behaviour, XMM-Newton data have unveiled a surprising diversity. Understanding the reason(s) behind such diversity is the challenge for the next decade of X-ray observations. (C) 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.