  It is generally regarded that the bulk of cosmic rays originate in the Galaxy
and that those below the 'knee' (the rapid steepening in the energy spectrum)
at a few PeV come from Galactic supernovae, the particles being accelerated by
the shocks in the supernova remnants. At higher energies, there are problems in
that conventional SNR - which surely constitute the bulk of the sources - have
a natural limit at a few tens of PeV (for iron nuclei). The question of the
origin of particles above this limit is thus an open one. Here we examine a
number of possibilities: a variety of supernovae and hypernovae, pulsars, a
Giant Galactic Halo and an Extragalactic origin.
  A relevant property of any model is the extent to which it can provide the
lack of significant irregularity of the energy spectrum. Although it is
appreciated that spectral measurements are subject to systematic as well as
random errors we consider that contemporary data are good enough to allow at
least some progress in this field.
  In the search for origin above PeV energies we conclude that shocks in the
Galactic Halo, whatever their source (Galactic wind, relativistic plasmoids -
'cannonballs', multiple shocks from supernovae etc.) are most likely, pulsrs
such as B0656+14 and hypernovae come a close second although such a suggestion
is not without its difficulties. What is most important is that trapping of
particles in the Halo is needed to reduce irregularities of the energy spectra
both below and above the 'knee' caused by the stochastic nature of supernova
explosions and other potential (discrete) Galactic sources.
  We argue that precise experimental studies of spectral 'irregularities' will
provide considerable help in the search for cosmic ray origin.
