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Axel Brandenburg is working in the field of astrophysical fluid dynamics and also has an interest in selected topics of astrobiology, particularly the question of homochirality at the origin of life. His main interests are concerned with magnetic field generation from turbulent motions with applications to the Sun and stars, accretion discs, galaxies, and the early Universe.

He produced the first compressible dynamo simulations in 1992. His work on accretion disc turbulence in 1995 was the first to show that the magneto-rotational and dynamo instabilities lead to a sustained doubly-positive feedback. The idea that large-scale primordial fields are the result of an inverse cascade goes back to his initial work of 1996. In 2005, he developed the concept of a distributed solar dynamo shaped by the near-surface shear layer. He contributed to the discovery of several new dynamo effects and found the production of magnetic spots as a generic result of stratification in hydromagnetic turbulence.

Since 2011, he has developed and applied new methods of determining magnetic helicity at the solar surface and in the solar wind. His work on the interpretation of stellar activity cycles revealed that all late-type stars younger than 2.3 billion years exhibit two cycle periods.

He is also responsible for the maintenance of the , a public domain code for solving partial differential equations on massively parallel machines.