This lecture reviews the strategies for measuring transverse spin phenomena in deep-inelastic scattering. Understanding such transverse polarisation phenomena in hadronic physics is a long-standing and intriguing problem. Despite of a wealth of experimental data on transverse spin asymmetries there is no measurement yet of the quark tranversity distribution which, together with the unpolarised and the helicity distribution, completes the three basic distributions to be measured in order to obtain a full description of the quark structure of the nucleon at leading twist. Modern developments in hadron physics emphasize the role of correlations of transverse momentum of partons and spin. Such spin-orbit correlations are described by a new class of transverse-momentum–dependent distribution and fragmentation functions (TMDs), which generalise the standard parton distributions. The information on spin-orbit correlations together with independent measurements related to the intrinsic motion of quarks will be the key to construct a complete picture of the internal structure of the nucleon going beyond the collinear approximation. Experiments that aim at pinning down various TMDs are currently running at Cern (Compass Collaboration), Desy (Hermes Collaboration), JLab, Kek and Rhic. Here, we will concentrate on the studies of transverse spin phenomena at the Hermes and Compass experiments in semi-inclusive deep-inelastic scattering on transversely polarised nucleon targets. After an overview of the analysis techniques we will present the first exciting results and give an attempt to interpret them.