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Free-electron-photon interaction, if it occurs inside an intense laser field, will be dominated by nonlinear Compton scattering ͑NLCS͒, which is quite different from the ordinary Compton scattering. The difference can be, for example, in the number of photons involved in one interaction. In this paper, by both analytical and numerical methods, we will explore in detail their characteristics from the viewpoint of energy exchange in the interaction. Based upon the well-displayed results, we are able to, furthermore, reveal some phenomena underlying NLCS and investigate the corresponding physical implications, such as the threshold effects in NLCS. That is, when QϭeE/(m e c)Ͼ0.1, the low-order NLCS will be depressed while the high orders will be excited. And when QϾ10, the high-order NLCS process will become dominant in the electron-photon interaction. As for QϾ100, the extra-high-order NLCS will be so strongly excited that the electron dynamics will enter a new regime. Also, we can make use of the obtained results to explain qualitatively the NLCS experiment by Bula et al. ͓Phys. Rev. Lett. 76, 3116 ͑1996͔͒. ͓S1050-2947͑99͒02106-X͔

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