Accreting Millisecond X-Ray Pulsars (AMXPs) are astrophysical laboratories
without parallel in the study of extreme physics. In this chapter we review the
past fifteen years of discoveries in the field. We summarize the observations
of the fifteen known AMXPs, with a particular emphasis on the multi-wavelength
observations that have been carried out since the discovery of the first AMXP
in 1998. We review accretion torque theory, the pulse formation process, and
how AMXP observations have changed our view on the interaction of plasma and
magnetic fields in strong gravity. We also explain how the AMXPs have deepened
our understanding of the thermonuclear burst process, in particular the
phenomenon of burst oscillations. We conclude with a discussion of the open
problems that remain to be addressed in the future.Comment: Review to appear in "Timing neutron stars: pulsations, oscillations
and explosions", T. Belloni, M. Mendez, C.M. Zhang Eds., ASSL, Springer;
[revision with literature updated, several typos removed, 1 new AMXP added
