Transition-metal-catalyzed cross-coupling reactions have been well-established as indispensable tools in modern organic synthesis. One of the major research goals in cross-coupling area is expanding the scope of the coupling partners. In the past decade, diazo compounds (or their precursors N-tosylhydrazones) have emerged as nucleophilic cross-coupling partners in C-C single bond or C = C double bond formations in transition-metal-catalyzed reactions. This type of coupling reaction involves the following general steps. First, the organometallic species is generated by various processes, including oxidative addition, transmetalation, cyclization, C-C bond cleavage, and C-H bond activation. Subsequently, the organometallic species reacts with the diazo substrate to generate metal carbene intermediate, which undergoes rapid migratory insertion to form a C-C bond. The new organometallic species generated from migratory insertion may undergo various transformations. This type of carbene-based coupling has proven to be general: various transition metals including Pd, Cu, Rh, Ni, Co, and Ir are effective catalysts; the scope of the reaction has also been extended to substrates other than diazo compounds; and various cascade processes have also been devised based on the carbene migratory insertion. This review will summarize the achievements made in this field since 2001.