It is well-established that fast-spinning millisecond pulsars are neutron stars recycled through accretion from binary companions. For most millisecond pulsars the accretion process has permanently ceased, and they are in binary systems with low-mass white dwarf companions. Follow-up observations of newly discovered gamma-ray sources from the Fermi Gamma-Ray Space Telescope have revealed a substantial population of "spider" millisecond pulsars with hydrogen-rich companions; these systems had mostly been missed in radio pulsar surveys. I will discuss the properties of neutron stars in these binaries and constraints on the maximum mass of neutron stars. I will also discuss new candidate members of the rare class of transitional millisecond pulsars, systems that switch between pulsar and accretion disk states on short timescales.
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