We review the theoretical studies of the Alfvén wave model of spicules and coronal heating, mainly based on the papers by Kudoh & Shibata (1999), Saito et al. (2001) and Moriyasu et al. (2004) which performed MHD numerical simulations of nonlinear Alfvén waves propagating along a magnetic flux tube in the solar atmosphere. Kudoh & Shibata (1999) and Saito et al. (2001) found that, if the root mean square of the perturbation is greater than ~ 1 km s−1 in the photosphere, (1) the transition region is lifted up to more than ~ 5000 km (i.e., the spicule is produced), (2) the energy flux sufficient for heating the quiet corona (~ 3.0 × 105 ergs s−1 cm−2) is transported into the corona by Alfvén waves. Moriyasu et al. (2004) demonstrated that a hot corona is created in an initially cool loop as a result of the nonlinear Alfvén waves produced near the photosphere. We conclude that the nonlinear Alfvén wave model is the promising model of spicules and coronal heating.

Understanding the mechanism that causes the emergence of magnetic flux from the solar interior to the atmosphere, the drastic changes in the properties of the matter and magnetic fields along the rise and the interplay of dynamic and resistive phenomena that shape the emerged regions is one of the major open tasks in solar physics. Important advances are being made both in the theoretical modelling and in the observation of the emergence events. This review concentrates on recent advances through 3D numerical experiments carried out with massively parallel MHD and radiative transfer codes.

Evidence of coronal oscillations over the interior of supergranular cells was found through SUMER observations. The observations are rasters of quiet Sun regions and the oscillations were detected, in the Ne ${\sc viii}\, 770 \AA$ Doppler maps, as a characteristic pattern. It should be noted that the Ne ${\sc viii}\,$ ion has coronal formation temperature (650 000 K) and that reports of oscillations in the quiet Sun corona are scarce. Magnetic extrapolation from MDI magnetogram showed that at the location where the oscillation was detected, the gas and magnetic pressures get equalized ($\beta$=1) higher in the atmosphere, compared to the surrounding, non oscillating quiet Sun. This could indicate a non-compressible wave propagating inside the gas dominated medium of the cell causing the detected oscillation.

We analyzed brightness variations in widespread dimming regions occurred in several major eruptive events in 2003 and 2005 resulted in fast halo CMEs. In all cases brightness of remote dimming regions show some pre-eruptive growth, then gradual and fast decrease to minimum. The time interval of maximal decrease overlaps with X-flare peak and LASCO CME onset. Brightness variations in some dimmed regions are highly correlated before the CME onset and much less – after. It suggests a break of magnetic connectivity between previously linked coronal structures. Dimmings develop similar at 175 and 195 Å being shallower and sometimes delayed at 304 Å. In large-scale region (L$>$0.5 $R_\odot$) dimming propagates with a speed of $\sim$ 250 km/s which is typical for EIT-waves.