In this talk, the operation of error diffusion for digital halftoning is described, and a linear gain model for the quantizer is employed which accurately predicts sharpening seen in error diffused images. New results are presented that explain an effect published in 1991 (R. Eschbach and K. Knox, ``Error-diffusion algorithm with edge enhancement,'' J. Opt. Soc. Am. A., vol. 8, pp. 1844-1850, Dec. 1991) that allows the sharpening of an error diffusion scheme to be manipulated by changing a single parameter. We use this result to further corroborate the linear gain model of the quantizer. A simple inverse halftoning scheme is presented that gives excellent visual results at a low computational cost (T. D. Kite, N. Damera-Venkata, B. L. Evans, and A. C. Bovik, ``A High-Quality, Fast Inverse Halftoning Algorithm for Error Diffused Halftoned Images'', Proc. IEEE Int. Conf. on Image Processing, Oct. 4-7, 1998, submitted.) Finally, we describe the ongoing research effort to obtain objective measures of subjective quality for both halftoned and inverse halftoned images, under a common framework.