Orbits around the two close collinear Sun-Earth Lagrange points have been utilized in recent decades for many solar and astronomical missions to exploit the observational advantages. DSCOVR is the first satellite to observe Earth continuously from the vicinity of the L1 point and is filing a crucial gap in Earth observations with its vast collection of polar, geosynchronous and some retrograde low inclination orbits. Spacecraft orbiting Venus in the last four decades have provided us with a wealth of information and many unanswered questions, which cannot be addressed adequately by observing from polar or near equatorial orbits around the planet. The Sun-Venus collinear Lagrange points L1 (sunward) and L2 (behind the planet from the Sun) points are key vantage points located about a million km away from the planet along the direction to the Sun which enable continuous monitoring of the planet's day and night hemispheres. As spacecraft positions at L1 and L2 points are unstable, they can be inserted in orbits around them to observe Venus over a small range of phase angles unlike any Venus orbiter observations which cover 0–180° solar phase angle twice each orbit for a very long time with minimal station keeping costs. To help better understand Venus, we propose that monitoring Venus continuously at nearly the same phase angle from the vicinity of L1 and L2 Lagrange points is critical. Such Lagrange orbiters around Sun-Venus L1 and L2 points can provide crucial information continuously about the evolution and variability of: (i) reflectance of the global cloud cover, (ii) the night side cloud cover opacity, (iii) surface activity, and (iv) interaction of planet's atmosphere with the solar wind, and loss of atmosphere. In addition, the two Lagrange orbiters can provide a crucial continuous communications capability for relaying data from in-situ atmospheric or surface platforms. Well instrumented missions to L1 and L2 points of Venus would significantly improve our understanding Earth's perplexing neighbor by obtaining continuous record of data on the day and night hemispheres not available from Venus orbiting missions.