Alfvén made many contributions to plasma physics, including theories describing the behavior of aurorae, the Van Allen radiation belts, the effect of magnetic storms on the Earth's magnetic field, the terrestrial magnetosphere, and the dynamics of plasmas in the Milky Way galaxy.

[4] In 1937, Alfvén argued that if plasma pervaded the universe, it could then carry electric currents capable of generating a galactic magnetic field.

[8] Many physicists regarded Alfvén as espousing unorthodox opinions[9] R. H. Stuewer noting that "... he remained an embittered outsider, winning little respect from other scientists even after he received the Nobel Prize..."[10] and was often forced to publish his papers in obscure journals.

Alfvén recalled: When I describe [plasma phenomena] according to this formalism most referees do not understand what I say and turn down my papers.

With the referee system which rules US science today, this means that my papers are rarely accepted by the leading US journals.

Many of his theories about the solar system were verified as late as the 1980s through external measurements of cometary and planetary magnetospheres.

However, Alfvén himself noted that astrophysical textbooks poorly represented known plasma phenomena: A study of how a number of the most used textbooks in astrophysics treat important concepts such as double layers, critical velocity, pinch effects, and circuits is made.

It is found that students using these textbooks remain essentially ignorant of even the existence of these concepts, despite the fact that some of them have been well known for half a century (e.g, double layers, Langmuir, 1929; pinch effect, Bennet, 1934).

Alfvén believed the problem with the Big Bang was that astrophysicists tried to extrapolate the origin of the universe from mathematical theories developed on the blackboard, rather than starting from known observable phenomena.

"[16] Alfvén was also interested in problems in cosmology and all aspects of auroral physics, and used Schröder's well known book on aurora, Das Phänomen des Polarlichts.

Alfvén was one of the few scientists who was a foreign member of both the United States and Soviet Academies of Sciences.