Near-IR emission is the best tracer of the old, evolved stellar population in galaxies and, at low redshift, rest frame emission between ~2μm and ~3.5μm is the best tracer of stellar mass. Hence, near-IR emission is closely connected to the assembly histories of galaxies. Observational studies of the shapes of K-band (2.2μm) luminosity functions (LFs) have resulted in mixed conclusions. Some studies suggest that the shape of the K-band LF for field galaxies is similar to that of cluster galaxies, while others have found considerable differences between the K-band LFs for cluster and field galaxies. In addition, studies of galaxies in ΛCDM simulations have often found that the simulations have difficulty reproducing the observed K-band LFs. Here, the K-band LFs of galaxies in the Illustris TNG300-1 simulation will be presented and will be compared to known constraints on the K-band LFs for observed galaxies. The preliminary conclusions are as follows. At low redshift, the shape of the K-band LF of TNG300-1 field galaxies differs little from that of cluster galaxies, and there is little evolution in the shape of the K-band LFs between z=0.5 and z=0.0. In contrast to observed galaxies, the K-band LFs of TNG300-1 galaxies are not well-fitted by Schechter functions. The K-band LFs of TNG300-1 cluster galaxies show a strong dependence on location within the cluster (i.e., clustercentric radius), as well as a strong dependence on intrinsic optical color (i.e., red vs. blue cluster galaxies). At z=0, the shape of the LF for bright (Mk < -18), red TNG300-1 cluster galaxies agrees well with observations and a Schechter-type LF. At fainter magnitudes, the LF for red TNG300-1 decreases steeply below that of a Schechter function. Conversely, the shape of the LF for faint (Mk > -20), blue TNG300-1 cluster galaxies at z=0 agrees well with observations and a Schechter function. Given that galaxy evolution is the most dynamic within high density regions of space, these results may provide insight for future modifications of galaxy formation and evolution algorithms that would yield better agreement between the observed and simulated universe.