The carrier density in solids plays an important role for the electronic and optical properties. It determines the position up to which electronic bands are filled. It also fixes the inter-particle distance and hence the carrier-carrier interaction strength. For two dimensional materials, the carrier density can be tuned by the field effect. Accessing a wide density range represents a powerful approach to explore interaction induced physics. Recently, ionic liquid and polymer electrolyte gating have emerged, which offer unprecedented control over the carrier density. Here, we study the electronic properties of thin oxides, oxide heterostructures and exfoliated two-dimensional crystals such as graphene, boron-nitride, molybdenum-disulfide and iron-based superconductors in the field effect geometry with electrolyte gating. We address, among other questions, whether it is possible to induce, destroy or modify superconducting behavior. The use of the field effect to change the density is superior to doping or intercalation as structural changes are avoided. Density dependent studies can be performed on one and the same sample and difficulties related to the incorporation of a large or varying number of dopants are absent.