Ground-based optical/IR interferometers have provided strong support to the space-based astrometric mission Hipparcos ever since the Hipparcos instrument was in operation in 1989. Interferometric observations also produced critical corrections of orbital motion to many targets, including radio stars, which link the Hipparcos system to the International Celestial Reference Frame (ICRF). In particular, orbital parallax from interferometers confirmed the 10% bias of the Pleiades distance from Hipparcos, and thus avoids revision of classical astronomy. Significant offsets and errors of Hipparcos parallax introduced by binary jitters are demonstrated in this work. By comparing the Hipparcos results with long baseline interferometry and other techniques including spectroscopy, multi-color photometry, Main-Sequence fitting, light curve measurements, Lunar occultation, Fine Guidance Sensor, etc., systematic biases and uncertainties of Hipparcos parallaxes are investigated and analyzed. We have established good models for major error sources of Hipparcos parallax, such as zonal bias, binary jitters, and luminosity-dependent errors. The lessons learned from the systematic biases of Hipparcos parallax are valuable to future space missions like SIM and Gaia.