Landscape of interactive proof systems My first question is whether an interactive proof system characterisation is known for all the classic complexity classes. I would call P, NP, PSPACE, EXP, NEXP,EXPSPACE, recursive and recursively enumerable functions classic (among others). Specifically,is an interactive proof system characterisation known for recursive and recursively enumerable functions?

I only know that IP = PSPACE and that MIP = NEXPTIME. By `know'  means I understand the definitions of objects on both sides of the equality and possibly understand the equality.

My second question is whether there is a graphical summary of different types of interactive proof systems and the complexity classes they characterise.

Specifically, I would like a reference to a figure similar to Immerman's picture of description complexity characterisations.
NP is ofter characterized as a proof system in which the prover sends a polynomial-length proof to a deterministic polynomial-time verifier, and after which there is no interaction. The class of recursively enumerable languages can be characterized similarly by replacing "polynomial" with "finite".

Also, since the class of recursive languages R is the intersection of RE and coRE, you can characterize R as a proof system in which an all-mighty prover can convince a finite time verifier both in the validity of correct claims and in the invalidity of false claims.

The class EXP has a characterization in terms of a proof system with "competing provers" - i.e., a proof system in which there is a prover that tries to convince the verifier that the claim is true and a refuter that tries to convince the verifier that the claim is false. See the paper "Making games short" of Feige and Kilian for more details.