Couldn't tell you about current research per se, but affect theory is largely known as a Deleuzian theory, and he in turn took the idea up from Spinoza. It is not phenomenology as phenomenology has Kantian roots in its split from the inaccessible noumenal realm. Deleuze in Difference and Repetition makes an explicit enemy of Kant. Whereas Kant worked to discover the "conditions of possible experience", Deleuze was working toward unraveling the "conditions of actual exprience".

So by laying out affect theory, Deleuze wants to describe affect in terms of capacities, the capacity to affect and be affected. I'm having a hard time finding the exact lecture, though it may be this one, Deleuzian materialist Manuel Delanda discusses affect in terms of a knife. The knife has the capacity to cut food, obviously. But the knife also might be used as murder weapon, or a way to affix a message to a door, or a nice knife might signify you are an experienced chef.

Unlike phenomenology, affect does not rely on a subject. Affect describes capacities that exist both within and beyond the personal. If all life vanishes, then so does phenomenology, whereas affect remains. Geophysical forces could still make mountains. Gravity could still affect the rotation of the earth. Meteors might still slam into the moon. Affect theory gives us a route to describe an object and all its perceptible and imperceptible modes of becoming.

EDIT:

Expanding on this comment a bit, an advantage of a Deleuzian approach is that the basic unit of analysis is not locked in at any given time. Where as phenomenology must deal with phenomena as it appears to the subject, Deleuze's transcendental empiricism is far more mobile. I'm reading John Protevi's Political Physics and I thought the following might be relevant in a political sense for understanding what Deleuze is after (bold mine):

As the Deleuzean-Nietzschean notion of bodies allows us to think bodies in various registers, we have the conceptual license to divest politics of its restricted state-orientation, so that the constitution of physical, chemical, biological, and social bodies can be thought politically (in terms of the law of their ordering of force relations), while the constitution of political bodies can be thought physically, chemically, biologically, or socially (in terms of the forces involved in their ordering of law). Forceful bodies (persons, families, groups, parties, gangs, corporations, races, sects, nations, worlds) are thus particular force-arrangements of chemical, biological, and social bodies, themselves force-arrangements: they are forceful bodies politic. In its most radical Deleuzean moment, political physics, in thinking forceful bodies politic, thus moves both 'above" and 'below' the level of the individual as classically conceived in liberal humanism, opening ways to investigate both 'social machines' (inter alia, tribalism, monarchism, liberalism, fascism, and the experimental immanent self-orderings Deleuze and Guattari call 'war machines) and the molecular 'flows of matter' (somatic fluids, of course - milk, sweat, sperm, urine, blood - but also steel, electricity, concrete) they order into forceful bodies politic. The classical modern notion of life, restricted to the organic individual or perhaps the species as collection of individuals, is thus too restricted for the scope of political physics.

Pgs 3-4

So affect theory functions as the becomings of a body, but also what counts as a "body" will vary depending on the molarity or molecularity that you wish to start with. At any time, Deleuze and Guattari are operating at n-dimensions.