  Let $\mathbf{k}$ denote the totally ordered set (or chain) on $k$ elements.
The product $\mathbf{k}^t=\mathbf{k}\times\cdots\times\mathbf{k}$ is a poset
called a grid. This paper discusses several loosely related results on the
Ramsey theory of grids. Most of the results involve some application of the
Product Ramsey Theorem.
