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This is a review on subgaussian sequences of random variables, prepared forthe Mediterranean Institute for the Mathematical Sciences (MIMS). We firstdescribe the main examples of such sequences. Then we focus on examples comingfrom the harmonic analysis of Fourier series and we describe the connection ofsubgaussian sequences of characters on the unidimensional torus (or any compactAbelian group) with Sidon sets. We explain the main combinatorial open problemconcerning such subgaussian sequences. We present the answer to the analogousquestion for subgaussian bounded mean oscillation (BMO) sequences on the unitcircle. Lastly, we describe several very recent results that provide ageneralization of the preceding ones when the trigonometric system (or itsanalogue on a compact Abelian group) is replaced by an arbitrary orthonormalsystem bounded in $L_\infty$.

Subgaussian sequences in probability and Fourier analysis