I summarise the state of the scientific exploration of the structure of galaxy clusters and present two new studies, namely, I propose and test a novel method to model clusters by a joint X-ray, thermal Sunyaev-Zeldovich and lensing analysis, and I investigate the impact of baryonic physics on strong cluster lensing and cluster structure. The three-dimensional reconstruction methods I propose assume only axial symmetry of the cluster with respect to an arbitrarily inclined axis. Cluster gas density and temperature distributions are found from X-ray and Sunyaev-Zeldovich data. Cumulative total-mass profiles and three-dimensional gravitational potentials are then obtained from these gas reconstructions assuming hydrostatic equilibrium, or independently by a gravitational lensing analysis, neglecting it. Hydrostatic equilibrium is quantitatively probed by comparing the two. The methods are described in detail and shown to perform well on progressively realistic synthetic data. Previous strong cluster lensing studies neglected the impact of the intracluster gas. I investigate it comparing simulations including gas physics at different levels of complexity. I found that adiabatic gas leaves strong lensing cross sections unchanged or somewhat reduces them, depending on the artificial viscosity implementation, while cooling and star formation steepen core density profiles and increase strong-lensing efficiencies considerably.