  Members of the family of pulsar-like stars are distinguished by their
different manifestations observed, i.e., radio pulsars, accretion-driven X-ray
pulsars, X-ray bursts, anomalous X-ray pulsars/soft gamma-ray repeaters,
compact center objects, and dim thermal neutron stars. Though one may
conventionally think that these stars are normal neutron stars, it is still an
open issue whether they are actually neutron stars or quark stars, as no
convincing work, either theoretical from first principles or observational, has
confirmed Baade-Zwicky's original idea that supernovae produce neutron stars.
After introducing briefly the history of pulsars and quark stars, the author
summarizes the recent achievements in his pulsar group, including quark matter
phenomenology at low temperature, starquakes of solid pulsars, low-mass quark
stars, and the pulsar magnetospheric activities.
