Title: Solar Magnetic Fields and their Helicity. Alexei A. Pevtsov National Solar Observatory Abstract: It has been said that without magnetic field the Sun would be a "boring" star. Indeed, the magnetic fields are at the origin of every solar active phenomenon. They are present on the spatial scales of elementary flux tubes (<0.1 Mm), the magnetic network, sunspots (30 Mm), coronal holes (few hundred Mm), and the Sun as a whole. The field is generated by the solar dynamo operating at the base of the convection zone. At the surface, stressed magnetic fields cause solar flares and coronal mass ejections (CMEs), which "cast away" solar plasma into interplanetary space. CMEs may trigger geomagnetic storms in the magnetospheres of Earth and other planets. The origin of the magnetic fields, their evolution, and topology may be better understood by studying the magnetic helicity (twist, handedness). Among other things, helicity allows inference of properties of dynamo and the turbulent convection below the surface. It may also be used in understanding the magnetic reconnection and forecasting the severity of geomagnetic storms. Recently, the concept of helicity was applied to the planetary, stellar, and galactic dynamo and to the jets from the accretion disks. I will review the properties of the solar magnetic fields and provide the examples of recent applications of magnetic helicity concept in solar and non-solar research.