In this review, I will discuss the main properties of transversity, the only chiral-odd collinear parton distribution function at leading twist. I will list the possible channels that can be explored to extract transversity from experimental data. I will describe our current knowledge of transversity with particular emphasys on its first Mellin moment, the tensor charge, and the puzzling comparison between phenomenological results and lattice computations. I will conclude by reminding the new useful data that still need to be included in phenomenological analyses, and by exploring the impact of future experimental setups.