Relation between interactive proof systems (IP), NP, coNP, PSPACE
IP = PSPACE is a famous result (and indeed paper) by Adi Shamir in 1992.

Furthermore, we clearly have NP $\subseteq$ PSPACE and coNP $\subseteq$ PSPACE, but we don't know how NP relates to coNP.  There are several reasons to believe that determining the relationship between NP and coNP is difficult, some of which are discussed in this recent thread.