Babcock–Leighton process, in which the poloidal field is generated through the decay and dispersal of tilted bipolar magnetic regions (BMRs), is observed to be the major process behind the generating poloidal field in the Sun. Based on this process, the Babcock–Leighton dynamo models have been a promising tool for explaining various aspects of solar and stellar magnetic cycles. In recent years, in the toroidal to poloidal part of this dynamo loop, various nonlinear mechanisms, namely the flux loss through the magnetic buoyancy in the formation of BMRs, latitude quenching, tilt quenching, and inflows around BMRs, have been identified. While these nonlinearities tend to produce a stable magnetic cycle, the irregular properties of BMR, mainly the scatter around Joy’s law tilt, make a considerable variation in the solar cycle, including grand minima and maxima. After reviewing recent developments in these topics, I end the presentation by discussing the recent progress in making the early prediction of the solar cycle.

We consider several tracers of magnetic activity that separate cycle-dependent contributions to the background solar magnetic field from those that are independent of the cycle. The main message is that background fields include two relative separate populations. The background fields with a strength up to 100 Mx cm−2 are very poorly correlated with the sunspot numbers and vary little with the phase of the cycle. In contrast, stronger magnetic fields demonstrate pronounced cyclic behaviour. Small-scale solar magnetic fields demonstrate features of fractal intermittent behaviour, which requires quantification. We investigate how the observational estimate of the solar magnetic flux density B depends on resolution D in order to obtain the scaling In BD = −k In D + a in a reasonably wide range. The quantity k demonstrates cyclic variations typical of a solar activity cycle. k depends on the magnetic flux density, i.e. the ratio of the magnetic flux to the area over which the flux is calculated, at a given instant. The quantity a demonstrates some cyclic variation, but it is much weaker than in the case of k. The scaling is typical of fractal structures. The results obtained trace small-scale action in the solar convective zone and its coexistence with the conventional large-scale solar dynamo based on differential rotation and mirror-asymmetric convection. Here we discuss the message for solar dynamo studies hidden in the above results.

Several uncertain helioseismic findings of potential interest to Jüri about the solar convection zone are briefly discussed, along with some personal optimistic hopes for the future.

The heliospheric magnetic field and the solar wind are behaving differently in the current solar minimum, compared to the previous minimum. The radial component of the heliospheric magnetic field, and thus the average value of the component of the solar magnetic field that opens into the heliosphere, the so-called open magnetic flux of the Sun, is lower than it was in the previous solar minimum; in fact, lower than in any previous solar minimum for which there are good spacecraft observations. The mass flux, the ram pressure, and the coronal electron temperature as measured by solar wind charge states are also lower in the current minimum compared to the previous one. This situation provides an opportunity to test some of the concepts for the behavior of the heliospheric magnetic field and the solar wind that have been developed; to improve these theories, and to construct a theory for the solar wind that accounts for the observed behavior throughout the solar cycle, including the current unusual solar minimum.

The solar magnetic cycle affects all levels of the Sun including the convection zone, photosphere, chromosphere and corona. Recent advances in solar space missions (Yohkoh, SOHO and others) and, also, ground-based observations provide us an excellent opportunity to investigate solar magnetic activity in detail, and to draw a new picture of the solar magnetic cycle. Magnetic field appears on the solar surface as a result dynamo processes in the convection zone, and forms bipolar complexes of solar activity. These complexes can be seen in the photosphere as dark sunspots surrounded by the bright plages extended into chromosphere, with arcades of coronal loops best observed in EUV and soft X-rays. The coronal loops reflect the large-scale magnetic structure of complexes of activity. The new data reveal fundamental changes in the magnetic topology during the solar cycle, and details of the polar magnetic field reversals occurring near the sunspot maximum. The solar synoptic maps obtained from the photospheric and coronal data display a close correlation between the erupted magnetic flux and coronal emissions and show large-scale magnetic connectivities. The brief review of solar cycle studies is presented.