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This paper investigates the role that nonlinear camera response functions (CRFs) have on image deblurring. In particular, we show how nonlinear CRFs can cause a spatially invariant blur to behave as a spatially varying blur. This can result in noticeable ringing artifacts when deconvolution is applied even with a known point spread function (PSF). In addition, we show how CRFs can adversely affect PSF estimation algorithms in the case of blind deconvolution. To help counter these effects, we introduce two methods to estimate the CRF directly from one or more blurred images when the PSF is known or unknown. While not as accurate as conventional CRF estimation algorithms based on multiple exposures or calibration patterns, our approach is still quite effective in improving deblurring results in situations where the CRF is unknown.