A theorem of Henry Helson shows that for every ordinary Dirichlet series a n n −s with a square summable sequence (a n ) of coefficients, almost all vertical limits a n χ(n)n −s , where χ : N → T is a completely multiplicative arithmetic function, converge on the right half-plane. We survey on recent improvements and extensions of this result within Hardy spaces of Dirichlet series -relating it with some classical work of Bohr, Banach, Carleson-Hunt, Cesàro, Hardy-Littlewood, Hardy-Riesz, Menchoff-Rademacher, and Riemann.