Gravity currents are buoyancy-driven flows having a significant impact on the environment and human life. They can be observed in a vast range of natural and anthropogenic scenarios, such as seawater and freshwater, the atmosphere, or industrial processes. Gravity currents transport sediments, nutrients, and oxygen in water bodies but they are also often dramatically involved in the spreading of contaminants and can represent a severe hazard to humans and infrastructures. The relevance of these phenomena has motivated extensive research on gravity currents such as the present study which addresses two main different research objectives. The first objective of this research concerns the modeling of gravity currents with Shallow Water Equations (SWE). Large Eddy Simulations data of continuously-fed gravity currents are used to discuss how the chosen definition of current depth affects the value of the coefficients appearing in the SW continuity and momentum equations due to the non-uniformity of the vertical distribution of flow variables. Moreover, the implications that different definitions of current depth have on research findings and entrainment parameterization are discussed. This analysis showed that coefficients appearing in the momentum equation might significantly (up to $30\%$) differ from one, depending on the chosen current depth definition. On the contrary, the coefficients appearing in the continuity equation were shown to be very close to one. The second main research objective was to study how the mean and turbulent structure of a density current changes when it propagates over a porous substrate and to characterize the volume exchanges occurring at its lower interface. Experiments were carried out in the Laboratory of Hydraulic Constructions at EPFL to reproduce continuously-fed density (saline) currents, which propagated first over a smooth horizontal bed and then over a porous substrate of limited length. Inflow discharge, initial excess density, substrate porosity, and downstream confinement of the substrate were systematically varied. An image analysis technique was developed to monitor the flow density evolution above the substrate and within its pores. Simultaneously, an Acoustic Doppler Velocimetry Profiler acquires a quasi-instantaneous 3D vertical velocity profile over the substrate. Experimental results showed that, after an initial phase during which the current sinks into the substrate, freshwater entrainment from the substrate pores starts. Consequently, a mixing layer gradually forms at the lower boundary of the current. Its presence affects the mean density, mean velocity, and turbulent field primarily in the near-bed region, where buoyancy contributes to turbulent kinetic energy generation together with shear. Moreover, at the porous substrate interface, buoyancy instabilities enhance the bed-normal momentum flux, increasing the bulk flow resistance. As a consequence, although the no-slip boundary condition results in lower friction losses, the shear velocity increases with the porosity of the substrate. In addition, experimental measurements allowed to quantify the current volume loss and the ambient-fluid entrainment from the substrate pores. The main drivers of these exchanges are discussed. The study of the entrainment of ambient-fluid from the bottom is fundamental to understand and model the resuspension of substances, such as nutrients and pollutants, present in the porous substrates.