  We study the generic and typical ranks of 3-tensors of dimension l x m x n
using results from matrices and algebraic geometry. We state a conjecture about
the exact values of the generic rank of 3-tensors over the complex numbers,
which is verified numerically for l,m,n not greater than 14. We also discuss
the typical ranks over the real numbers, and give an example of an infinite
family of 3-tensors of the form l=m, n=(m-1)^2+1, m=3,4,..., which have at
least two typical ranks.
