  In this paper we review the notions of gonality and Clifford index of an
abstract curve. For a curve embedded in a projective space, we investigate the
connection between the \ci of the curve and the \gc al properties of its \emb.
In particular if $C$ is a curve of degree $d$ in ${\P}^3$, and if $L$ is a
multisecant of maximum order $k$, then the pencil of planes through $L$ cuts
out a $g^1_{d-k}$ on $C$. If the gonality of $C$ is equal to $d-k$ we say the
gonality of $C$ can be computed by multisecants. We discuss the question
whether the \go of every smooth ACM curve in ${\P}^3$ can be computed by
multisecants, and we show the answer is yes in some special cases.
