In the last twelve years there has been much study of what happens when an algebraic curve in $n$-space is intersected with two multiplicative relations $x_1^{a_1} \cdots x_n^{a_n}~=~x_1^{b_1} \cdots x_n^{b_n}~=~1 \eqno(\times)$ for $(a_1, \ldots ,a_n),(b_1,\ldots, b_n)$ linearly independent in ${\bf Z}^n$. Usually the intersection with the union of all $(\times)$ is at most finite, at least in zero characteristic. In Oxford nearly three years ago I could treat a special curve in positive characteristic. Since then there have been a number of advances, even for additive relations $\alpha_1x_1+\cdots+\alpha_nx_n~=~\beta_1x_1+\cdots+\beta_nx_n~=~0 \eqno(+)$ provided some extra structure of Drinfeld type is supplied. After reviewing the zero characteristic situation, I will describe recent work, some with Dale Brownawell, for $(\times)$ and for $(+)$ with Frobenius Modules and Carlitz Modules.
