In this talk, I will discuss a convex formulation of the clustering problem and its generalization to biclustering of matrices and more broadly to co-clustering of multiway arrays or tensor data. The key advantage in formulating clustering as a convex program is that doing so addresses well-known issues of instability and parameter selection that plague mainstream approaches. The formulation also admits a simple first order iterative algorithm for solving the problem with global convergence guarantees. We also provide a finite sample bound for the prediction error of our convex co-clustering (CoCo) estimator.  Finally, we illustrate the utility of this formulation and algorithm in biclustering high throughput bioinformatics data and in co-clustering click-through contingency tables of online advertising data.