Lead halide perovskite nanocrystals (NCs) have been widely studied for application in optoelectronic devices due to their excellent optical properties and low-cost synthesis. However, the toxicity of lead and the poor stability of the NCs hindered their practical applications. Sn2+-based perovskite with low toxicity was first developed; however, the Sn2+-based perovskite NCs are unstable in air and oxidize easily. Recently, air-stable lead-free perovskite NCs have been developed and received increasing attention. Unfortunately, the optical and optoelectronic properties of these lead-free halide perovskite NCs are generally far worse than those of lead-perovskite NCs. Understanding the charge-carrier dynamics of semiconductors is crucial to improve their optical properties. In this Account, we mainly review our recent research progress on the study of charge-carrier dynamics in air-stable lead-free perovskite NCs. The exciton trapping followed by nonradiative recombination was the major carrier relaxation pathway and resulted in a low photoluminescence quantum efficiency (PLQE). A feasible route for passivating surface traps and tuning the self-trapped excitons from "dark" (nonradiative) to "bright" (radiative) was proposed. Through this strategy, the PLQE could be increased over 100-fold. In addition, we have compared several photophysical properties of lead-free perovskite NCs with that of lead perovskite NCs, such as charge-carrier relaxation, exciton-phonon coupling, and hot-carrier cooling. In 2017, we reported the synthesis, optical properties, and charge-carrier dynamics of Cs3Bi2X9 (X: Cl, Br, I) NCs. The Cs3Bi2Br9 NCs exhibited clear exciton trapping processes with time scales in the range of 2-20 ps. The fast trapping processes could be passivated via the use of surfactants (such as oleic acid), and the PLQE increased over 20-fold (from 0.2% to 4.5%). The low PLQE may be due to the reduced dimensionality of Cs3Bi2Br9 (2D) compared with the 3D cubic perovskite structure of CsPbBr3. We next reported double perovskite Cs2AgSb1-yBiyX6 (X: Br, Cl; 0 ≤ y ≤ 1) NCs, which exhibited a similar 3D cubic perovskite structure to that of the lead-perovskite NCs. The charge-carrier dynamics indicated that the sub-band-gap exciton trapping processes were dominated by ultrafast (∼1-2 ps) intrinsic self-trapping and trapping at surface defects (∼50-100 ps). While trapping at surface defects can be passivated using surfactants, the self-trapping processes is due to the giant carrier-phonon coupling effect. By designing direct band gap double perovskite NCs to tune the sub-band-gap trapping processes, bright dual-color emission was achieved. Furthermore, the violet PLQE could be improved to 36.6%, which is comparable to that in lead halide perovskite NCs. We hope this Account will deepen the understanding of the charge-carrier dynamics in lead-free perovskite NCs and guide the design of high-performance lead-free perovskites.