Sunspots show oscillations of velocity, of intensity (that is of thermodynamic quantities), and possibly of the magnetic field. The oscillations are observed in different period bands (in particular around 2–3 min, 5 min, and > 20 min), at all height levels of the sunspot atmosphere, and with different spatial distributions and characteristic phase relations. In the present invited talk some basic properties of the observed umbral oscillations are shortly reviewed, and different approaches to the modeling and interpretation are discussed.