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The noise stability of a Euclidean set is a well-studied quantity. This quantity uses the Ornstein-Uhlenbeck semigroup to generalize the Gaussian perimeter of a set. The noise stability of a set is large if two correlated Gaussian random vectors have a large probability of both being in the set. We will first survey old and new results for maximizing the noise stability of a set of fixed Gaussian measure. We will then discuss some recent results for maximizing the low-correlation noise stability of three sets of fixed Gaussian measures which partition Euclidean space. Finally, we discuss more recent results for maximizing the low-correlation noise stability of symmetric subsets of Euclidean space of fixed Gaussian measure. All of these problems are motivated by applications to theoretical computer science.