The structure of the "30 nm chromatin fiber", as observed in vitro, has been a matter of controversy for 30 years. Recent studies with new and more powerful techniques give some promise for resolution. However, this will not necessarily inform us as to the in vivo structure, which may be both heteromorphic and dynamic. In this chapter, we briefly review the older conjectures and some more recent studies of special interest. We attempt to point out the remaining contradictions and hopeful lines of future research.