  We enumerate complex curves on toric surfaces of any given degree and genus,
having a single cusp and nodes as their singularities, and matching
appropriately many point constraints. The solution is obtained via tropical
enumerative geometry. The same technique applies to enumeration of real plane
cuspidal curves: We show that, for any fixed $r\ge1$ and $d\ge2r+3$, there
exists a generic real $2r$-dimensional linear family of plane curves of degree
$d$ in which the number of real $r$-cuspidal curves is asymptotically
comparable with the total number of complex $r$-cuspidal curves in the family,
as $d\to\infty$.
