The oldest and best established Swampland constraint is perhaps the idea that there are no global symmetries in quantum gravity. Traditionally, this idea has been regarded as not strong enough to strong constraints at low energies, since the quantum gravity symmetry breaking effects could be extremely weak. I will describe recent progress in Swampland, in conjunction with developments in generalized and non-invertible symmetries, which have led to the discovery of new branes in string theory, new mechanisms to engineer small couplings in string theory, and even ruling out some effective field theories in higher dimensions.

It is natural to expect that quantum gravity is not directly relevant at the low energies which experimentally accesible today, since the Planck scale is many orders of magnitude above the electroweak scale. However, mounting evidence coming from String Theory compactifications, general considerations based on black hole evaporation and holography suggest that there are some constraints that must be satisfied by low-energy effective field theories coupled to Einsteinian gravity. These constraints can in principle be used to rule out models at low energies or to connect with observations, an effort dubbed the "Swampland Program". I will review the program, its motivation, and recent advances.