Organic-catalysis microwaves
Here is an example of an entire online GoogleBook dedicated to the topic Microwave Assisted Organic Synthesis, apparently based on some 2,000 papers.
On page 3 of the cited reference, notes to quote:

Interaction between microwave radiation and solutions of polar molecule polar molecules may be adequately described using classical models, which may be derived from Maxwell's equations.

And further:

Although this analysis has concentrated on the oscillating components of the electromagnetic field of the microwave radiation,  it is also possible to get interaction between the oscillating magnetic field and the magnetic dipoles in the sample. The high-heating rates for Fe304 may be attributed to such interactions.

With respect to benefits, per page 23 to quote:

Reaction rates are generally very high and yields in many cases can be greatly improved, as competing side reactions can be minimized...

I would also add that the use of microwave-based dielectric heating is, at times, more than just fast and efficient and heating, as it can, in the presence of activated carbon, for example, introduce surface-based radicals into the reaction mix. See, for example, Generation of hydroxyl radical in aqueous solution by microwave energy using activated carbon as catalyst and its potential in removal of persistent organic substances.
As such, I described the general use of this new heating technology as microwave-assisted synthesis, and not per se, as catalytic, albeit depending on the reaction mix, it can be (per last cited reference).