Millisecond pulsars (MSPs) are formed by being spun-up (recycled) to rapid spin periods through accretion of matter and angular momentum from a non-degenerate companion. Studies of these systems provide essential insights into the physics of low-level accretion onto magnetized compact objects and the interactions between MSPs and their stellar and gaseous environment. The MSP population in the Galactic field is dominated by wide orbit MSP-white dwarf binaries, representing the end products of this recycling process. However, recent multiwavelength follow-up observations of unassociated Fermi γ-ray sources have revealed a subclass of MSP binaries in which recycling is apparently not yet complete. In this talk, I will outline some of the basic steps we take to identify and characterize candidate MSP binaries in the late stages of the recycling process, and will show a few systems whose unusual phenomenology and inferred evolutionary tracks suggest they are the first known systems in an expanding class of compact objects that are the progenitors of typical field MSP binaries.