In the 22nd century, they were suffering from a genetic disease which became a planet-wide epidemic. Several space shuttles were launched to search for warp-capable species which would assist them.
One shuttle was discovered by the Earth starship Enterprise, who offered their assistance. However, when Dr. Phlox discovered that the Menk, the Valakians evolutionary counterparts, were evolving the Enterprise left hoping that the Valakians would develop a cure on their own. (ENT episode: "Dear Doctor")
By 2236, the Valakian population had declined to a few hundred thousand, while the Menk became dominant, with their population reaching the tens of millions. They soon became part of the United Federation of Planets when they discovered warp-drive. (Star Trek: Star Charts)