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I'll review some results about Forbidden Configurations while introducing a conjecture. Let $F$ be a $k\times  l$ (0,1)-matrix. We define a matrix to be {\it simple} if it is a (0,1)-matrix with no repeated columns.  We say that a simple matrix $A$ has no $F$-{\it configuration} if no submatrix of $A$ is a row and column permutation of $F$. We are interested in the extremal function ${\hbox{forb}}(m,F)$ which is the maximum number of columns in an $m$-rowed simple matrix that has no $F$-configuration. This is equivalent to extremal set theory problem with configurations called {\it trace}.  A conjecture of Sali and A.
predicts the asymptotic behaviour of ${\hbox{forb}}(m,F)$ for any fixed $F$ as $m$ tends to infinity using some easy but seemingly important constructions.

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I'll discuss the conjecture as well as progress to its solution (joint work with Balin Fleming, Zoltan Furedi, Peter Keevash, and Attila Sali). In addition I'll mention some $F$ for which we have exact values of ${\hbox{forb}}(m,F)$ (adding credit to Farzin Barekat, Laura Dunwoody, Ron Ferguson, Jerry Griggs and Nima Kamoosi)
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