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.