Suppose X_1,...,X_k are n-dimensional Gaussian vectors with a given covariance structure. What is the partition of R^n into r sets of given Gaussian measures m_1,...,m_r which maximizes P[ (X_1,...,X_k) fall in the same part of the partition]? I will give an overview of what is known and conjectured about this question in various setups as well as various reasons for studying it and connections to classical isoperimetric problems.