The 3-min oscillations in the sunspot atmosphere are discussed, based on joint observing with the Transition Region and Coronal Explorer - TRACE and the Solar and Heliospheric Observatory - SOHO. We find that the oscillation amplitude above the umbra increases with increasing temperature, reaches a maximum for emission lines formed close to 1-2× 105 K, and decreases for higher temperatures. Oscillations observed with a high signal-to-noise ratio show deviations from pure linear oscillations. The results do not support the sunspot filter theory, based on the idea of a chromospheric resonator. Whereas the filter theory predicts several resonant peaks in the power spectra, equally spaced ~1 mHz in frequency, the observed power spectra show one dominating peak, close to 6 mHz. Spectral observations show that the transition region lines contribute less than 13 percent to the TRACE 171 Å channel intensity above the umbra. The 3-min oscillations fill the sunspot umbra in the transition region. In the corona the oscillations are concentrated to smaller regions that appear to coincide with the endpoints of sunspot coronal loops, suggesting that wave propagation along the magnetic field makes it possible for the oscillations to reach the corona.