Аннотация:Magnetic fields on the Sun can be measured by spectroscopic methods only in transparent parts of its atmosphere. Our knowledge about magnetic fields in the solar interior is based on a number of assumptions, indirect measurements and their interpretations, which are highly uncertain and model dependent. Because of this, different authors present estimates differing by orders of magnitude for this important physical quantity. Available theories can not eliminate this uncertainty without more sophisticated observational input information. The question about magnetic fields inside the Sun will remain without definite answer in future if no physical ideas will appear how to measure internal solar magnetic fields in a more direct way than now. We review existing and possible new approaches to this unsolved problem. This study was partially supported by the RFBR grants 07-02-00147, 06-05-64500, INTAS 03-51-6202 and MSU Interdisciplinary Scientific Project. It is also fulfilled as a part of the Programs of the Russian Academy of Sciences: "Origin and evolution of stars and galaxies" (P-04), "Solar activity and physical processes in the Sun-Earth system" (P-16, Part 3) and "Plasma processes in the Solar system (OFN-16).