For over two decades the RECONS (REsearch Consortium On Nearby Stars, www.recons.org) group has been studying stars in the solar neighborhood with two primary goals: (1) to reveal key statistics about volume-complete samples of stars via comprehensive surveys, and (2) to push towards finding a nearby, habitable world. We are currently surveying ~5000 K dwarfs within 50 pc from the Sun for stellar, substellar, and planetary companions with three different techniques: Wide separation companions from precise Gaia astrometry, arcsec-milliarcsec companions with speckle imaging, and unresolved close companions with the radial velocity (RV) technique. Here we present progress on our RV survey of 304 K dwarfs, a sample that includes *ALL* the equatorial (DEC +30º to -30º) K dwarfs within 25 pc. We have used the CHIRON high-resolution spectrograph at the CTIO/SMARTS 1.5m for the past three years to acquire time-series RVs on each star with a least one-year baselines to precisions of ~7-10 m/s — this precision allows us to detect jovian-mass planetary companions. In combination with the observations done by other precise RV instruments, we have now completed coverage for 90% of our sample, with the remaining few requiring only a few more epochs. With these results we aim to overcome the limitations due to selection biases in previous planet searches, e.g., omitting stellar multiples, and unveil the occurrence and nature of the stellar, brown dwarf, and giant planet populations around K dwarf stars from a well defined volume-complete sample. This work has been supported by NSF grants AST-1517413, AST-1517824, AST-1909560, and AST-1910130 and the SMARTS Consortium.