the gonality of a smooth projective curve is the smallest degree of a map from the curve to the projective line. if a curve is embedded in projective space, it is natural to ask whether the gonality is related to the embedding. in my talk, i will discuss recent work with james hotchkiss. our main result is that, under mild degree hypotheses, the gonality of a complete intersection curve in projective space is computed by projection from a codimension 2 linear space, and any minimal degree branched covering of $p^1$ arises in this way.