This paper presents a cognitive perspective on the problem of using the Internet via screen readers. An empirical study shows similarities and dissimilarities between using the Internet via screen readers and via the standard graphical screen. In particular, spatial cognition is an important determinant of web task performance even in the absence of any visual cues. Backtracking behavior has a higher cost and impacts performance in a more negative way when using the Internet via screen readers as compared to the standard use. Selective reading can be used as an addition to the existing functionality of screen readers but more research is needed to prove the utility of such support mechanism. Computational cognitive modeling can be used in conceiving, testing and implementing cognitively informed support functionality in screen readers.