A vortex manipulator was a form of basic time travel developed by the Time Agency of the 51st century. The accuracy of travel the vortex provides is unclear, Jack Harkness arrived in 1869 when aiming for the late 20th century. The presence of a Time Lord during travel is somehow able to enhance the accuracy of the travel path, as the Doctor is able to guide Jack and Martha back from the future to within days of when he and Martha had last left, this may be related to the time senses of a Time Lord or simply greater understanding of time travel.
Although it was generally used by the Agency, the Family of Blood stole one to follow the Doctor around the universe. (DW: Human Nature) The Doctor considered it very primitive compared to a TARDIS, describing his TARDIS as a "sports car" to Jack Harkness's "space hopper".
Jack Harkness had his manipulator housed in a Time Agency wrist strap. (DW: Utopia)