We investigate evolutionary pathways leading to neutron star formation through the collapse of oxygen-neon white dwarf ( ONe WD ) stars in interacting binaries . We consider ( 1 ) non-dynamical mass transfer where an ONe WD approaches the Chandrasekhar mass leading to accretion-induced collapse ( AIC ) and ( 2 ) dynamical timescale merger-induced collapse ( MIC ) between an ONe WD and another WD . We present rates , delay times , and progenitor properties for two different treatments of common envelope evolution . We show that AIC neutron stars are formed via many different channels and the most dominant channel depends on the adopted common envelope physics . Most AIC and MIC neutron stars are born shortly after star formation , though some have delay times > 10 Gyr . The shortest delay time ( 25 - 50 Myr ) AIC neutron stars have stripped-envelope , compact , helium-burning star donors , though many prompt AIC neutron stars form via wind-accretion from an asymptotic giant branch star . The longest delay time AIC neutron stars , which may be observed as young milli-second pulsars among globular clusters , have a red giant or main sequence donor at the time of NS formation and will eventually evolve into NS + helium WD binaries . We discuss AIC & MIC binaries as potential gravitational wave sources for LISA . Neutron stars created via AIC undergo a LMXB phase , offering an electromagnetic counterpart for those shortest orbital period sources that LISA could identify . The formation of neutron stars from interacting WDs in binaries is likely to be a key mechanism for the production of LIGO/Virgo gravitational wave sources ( NS-NS and BH-NS mergers ) in globular clusters .