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We prove that the Hausdorff dimension of the graph of a prevalent continuousfunction is 2. We also indicate how our results can be extended to the space ofcontinuous functions on $[0,1]^d$ for $d \in \mathbb{N}$ and use this to obtainresults on the `horizon problem' for fractal surfaces. We begin with a surveyof previous results on the dimension of a generic continuous function.

The Hausdorff dimension of graphs of prevalent continuous functions