  Anomalous X-ray pulsars (AXPs) and soft gamma-ray repeaters (SGRs) are
enigmatic pulsar-like objects. The energy budget is the fundamental problem in
their studies. In the magnetar model, they are supposed to be powered by the
extremely strong magnetic fields (>~ 10^14 G) of neutron stars. Observations
for and against the magnetar model are both summarized. Considering the
difficulties encountered by the magnetar model to comfortably understand more
and more observations, one may doubt that AXPs and SGRs are really magnetars.
If they are not magnetar candidates (including magnetar-based models), then
they must be "quark star/fallback disk" systems.
