Probing the interiors of the gaseous giant planets in our solar system is not an easy task. It requires a set of accurate measurements combined with theoretical models that are used to infer the planetary composition and its depth dependence. The masses of Jupiter and Saturn are 317.83 and 95.16 Earth masses (M⊕), respectively, and since a few decades, it has been known that they mostly consist of hydrogen and helium. The mass of heavy elements (all elements heavier than helium) is not well determined, nor are their distribution within the planets. While the heavy elements are not the dominating materials inside Jupiter and Saturn, they are the key to understanding the planets’ formation and evolutionary histories. The planetary internal structure is inferred from theoretical models that fit the available observational constraints by using theoretical equations of states (EOSs) for hydrogen, helium, their mixtures, and heavier elements (typically rocks and/or ices). However, there is no unique solution for determining the planetary structure and the results depend on the used EOSs as well as the model assumptions imposed by the modeler. Major model assumptions that can affect the derived internal structure include the number of layers, the heat transport mechanism within the planet (and its entropy), the nature of the core (compact vs. diluted), and the location (pressure) of separation between the two envelopes. Alternative structure models assume a less distinct division between the layers and /or a non-homogenous distribution of the heavy elements. The fact that the behavior of hydrogen at high pressures and temperatures is not perfectly known and that helium may separate from hydrogen at the deep interior add sources of uncertainty to structure models. In the 21st century, with accurate measurements of the gravitational fields of Jupiter and Saturn from the Juno and Cassini missions, structure models can be further constrained. At the same time, these measurements introduce new challenges for planetary modelers.