Abstract: In this talk we revise a recently established Hardy inequality in twisted tubes on the background of transience of the Brownian motion. We begin by recalling the classical Hardy inequality and its relation to geometric, spectral, stochastic and other properties of the underlying Euclidean space. After discussing the complexity of the problem when reformulated for quasi-cylindrical subdomains, we focus on the prominent class of tubes. As the main result, we give a new proof of the Hardy inequality due to a twist of three-dimensional tubes of uniform cross-section.