This paper explores the idea that mRNAs are transported between their transcription and processing sites in the nucleus, and their translation and degradation sites in the cytoplasm, by a 'solid-state' process. The underlying assumption is that negligible quantities of mRNA and of mRNA precursors are in solution in vivo. Therefore, mRNA transport cannot be considered as movement in the aqueous phase of the cell. The main lines of experimental evidence supporting this 'solid-state' concept are summarized and related controversies are outlined. Three possible models for a solid-state transport mechanism are discussed: a direct transfer model, with receptors organized analogously to the components of a multienzyme complex; a motor-driven model, analogous to synaptic vesicle transport in axons; and an assembly-driven model which assumes net movement along a fibril resulting from differential activities at the poles. Qualitative evaluation indicates that each of these models has characteristic advantages and disadvantages. The possibility that other nucleocytoplasmic transport processes might operate by solid-state mechanisms is briefly discussed.