  We study the moduli of trigonal curves. We establish the exact upper bound of
${36(g+1)}/(5g+1)$ for the slope of trigonal fibrations. Here, the slope of any
fibration $X\to B$ of stable curves with smooth general member is the ratio
$\delta_B/\lambda_B$ of the restrictions of the boundary class $\delta$ and the
Hodge class $\lambda$ on the moduli space $\bar{\mathfrak{M}}_g$ to the base
$B$. We associate to a trigonal family $X$ a canonical rank two vector bundle
$V$, and show that for Bogomolov-semistable $V$ the slope satisfies the
stronger inequality ${\delta_B}/{\lambda_B}\leq 7+{6}/{g}$. We further describe
the rational Picard group of the {trigonal} locus $\bar{\mathfrak T}_g$ in the
moduli space $\bar{\mathfrak{M}}_g$ of genus $g$ curves. In the even genus
case, we interpret the above Bogomolov semistability condition in terms of the
so-called Maroni divisor in $\bar{\mathfrak T}_g$.
