We present observational results from which we can determine azimuthal currents flowing across the magnetic field. Simple relations between the vertical current densities and the inclinations of the field are used to separate from each other the field-aligned component and the azimuthal component of current density. For
a relatively isolated flux bundle we obtain a total azimuthal current density of (7.8 ± 3,6)' 10-2 Am-2 and an azimuthal current of
(6,5 ± 3.0)‘ 10^^ A. The density of the Lorentz force acting amounts up to 1,1 -10-3 Nm-3.
We review the basic features of oscillations observed at different height levels in the sunspot atmosphere, moreover, various possibilities for a theoretical interpretation are discussed. In the umbra oscillation power is concentrated in severa] period bands
(3 min., 5 min., and ≥ 20 min.) which on their part are composed of closely packed peaks. The observed amplitudes and phases of velocity and of intensity oscillations depend in a characteristic way on the period and on the height. These features are used to look for the most probable physical mechanisms which could produce the different modes: At subphotospheric depths two independent resonators are acting. A resonator for slow, quasi-transveree waves can explain the lifetimes of umbral dots (≥ 20 min.), while a resonator for fast (acoustic), quasi-longitudinal waves could result in the umbral 5-min. oscillations. The acoustic resonator strongly couples with the slow-mode longitudinal resonator at photospheric and chromospheric heights, the latter produces the resonance peaks in the 3-min. band. Running penumbral waves can be explained by the transformation of 5-min, waves from the convective zone in the almost horizontal magnetic field. The interpretation of oscillations provides a new method of probing not only subphotospheric, but also atmospheric layers of sunspots (e.g., of determining temperature gradients), thus completing customary spectroscopic diagnostics.