Hardware-based track reconstruction in the CMS and ATLAS trigger systems for the high-luminosity upgrade of the LHC (HL-LHC) will provide unique capabilities. In this review, we present an overview of earlier track trigger systems at hadron colliders, in particular for the Tevatron CDF and DØ experiments. We discuss the plans of the CMS and ATLAS experiments to implement hardware-based track reconstruction for the HL-LHC. Particular focus is placed on the track trigger capability of the upgraded CMS experiment. We discuss the challenges and opportunities of this novel capability, review the alternatives that were considered for its implementation, and discuss its expected performance. The planned track trigger systems for CMS and ATLAS have different goals, and we compare and contrast the two approaches. Expected final online publication date for the Annual Review of Nuclear and Particle Science, Volume 70 is October 19, 2020. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.