Carbon dioxide (CO₂) is the dominant greenhouse gas and the most abundant and renewable C₁ resource. Therefore, the chemical fixation and conversion of CO₂ to high-value chemicals and materials is an intriguing strategy towards carbon neutrality and sustainable chemical industry. The direct carboxylation of C(sp)-H bonds with CO₂ has attracted great interest in the last decade as an atom-economic approach to propiolic acids, which have a wide range of applications in pharmaceuticals and advanced materials. This article provides a comprehensive review of this growing field of research. With a brief overview of non-catalytic carboxylation, the focus is on catalytic processes, which overwhelmingly involve metal catalysts, homogeneous or heterogeneous. The recently budding organocatalysis is also included. Critical comparisons and mechanism analyses are provided, along with personal perspectives for future studies.