However, academically, cultural evolution ought to be a kind of wasteland - in the sense that it has little or no content which is not shared by ordinary conventional evolutionary theory.
As Herbert Spencer put it - in 1862:
there are not several kinds of Evolution having certain traits in common, but one Evolution going on everywhere after the same manner.
The main differences between cultural and organic evolution turn out to be differences between memetics and genetics. Once those differences are accounted for, a theory of cultural evolution doesn't have a lot of theoretical work to do - since orthodox evolutionary theory already does most of the job required. I think that this issue has been poorly understood by many workers in the field.
My "differences remain exaggerated" article describes this problem. Misconceptions by researchers about how cultural evolution operates apparently led them to believe that there were considerable differences between the dynamics of organic and cultural evolution - and that we needed a new field of "cultural evolution" to study these differences. However, it turns out that these differences have been greatly exaggerated - that many of the perceived differences were illusory, and that most of the actual differences are in the memetics / genetics departments.
Apart from memetics, the other things needed are cultural ecology and ethology. However, there isn't much work for a theory of cultural evolution to do - once memetics is accounted for. Orthodox evolutionary theory has it covered. Memetics covers the field where the real action is.
Once you understand that culture evolves, the topic of "cultural genetics" is really the next thing on the horizon. Just as genetics followed evolution historically, so "cultural genetics" will follow "cultural evolution" during the modern Darwinian revolution. Of course, memetics enthusiasts have been working on the topic of how cultural elements mutate and recombine for decades - but it will be good to have an influx of new researchers into the field.