Thorne-Żytkow objects (TŻOs) are red supergiants with neutron cores. The energy source in TŻOs with low-mass envelopes (≲8 M⊙) is accretion onto the neutron core, while for TŻOs with massive envelopes (≲14 M⊙) it is nuclear burning via the exotic rp process. TŻOs are expected to form as a result of unstable mass transfer in high-mass X-ray binaries, the direct collision of a neutron star with a massive companion after a supernova or the collision of a neutron star with a low-mass star in a globular cluster. We estimate a birth rate of massive TŻOs in the Galaxy of ∼2 10−4 yr−1. Thus, for a characteristic TŻO lifetime of 105–106 yr there should be 20–200 TŻOs in the Galaxy at present. These can be distinguished from ordinary red supergiants because of anomalously high surface abundances of lithium and rp-process elements, produced in the TŻO interior. The TŻO phase ends when either the star has exhausted its rp-process seed elements or the envelope mass decreases below a critical mass (∼14 M⊙). Then nuclear burning becomes inefficient and a neutrino runaway ensues, leading to the dynamical accretion of matter near the core onto the neutron star and its spin up to spin frequencies of up to ∼100 Hz. The fate of the massive envelope is not entirely clear. If a significant fraction can be accreted onto the core, the formation of a black hole becomes likely. Part of the envelope may collapse into a massive disk which may ultimately become gravitationally unstable and lead to the formation of planets or even low-mass stars. We discuss the various possible outcomes and suggest a possible link between massive TŻOs and soft X-ray transients.