Chronic unit recording experiments conducted over the past two decades have identified many functional classes of neurons with saccade-related activity that reside in a host of brainstem nuclei. Older models of the saccadic system were based upon the properties of only a few of these functional types of neurons. They described the putative flow of signals through the brainstem circuitry and specified some, but not all, of the signal transformations to be performed. How the necessary computations were performed by neurons was not always explicit. Recent experiments investigating the neural control of saccadic eye movements and modifications of the original models are designed to fill in the details of the broad sketch of saccadic circuitry originally available. This review suggests one strategy for proceeding with this effort. Saccadic command signals observed in the SC require transformation to interface with the burst generators and motoneuron pools innervating the extraocular muscles. Specifying the signal transformations required for this interface should facilitate the design of experiments directed toward an understanding of the functional properties of cells located in nuclei intervening between the SC and the pulse/step circuitry, subsets of neurons that often have no role in models of the saccadic system. In this review, we hypothesize that neurons residing in various tectorecipient brainstem nuclei participate in one or more of the required signal transformations. The pathway from SC to cMRF and PPRF may be involved in the extraction of information about the amplitude and/or velocity of the horizontal component of oblique saccades. The pathway from SC to NRTP and cerebellar vermis may act selectively to generate signals compensating for the presaccadic orbital position. Finally, the activity of LLBNs and MLBs discharging maximally before oblique saccades may form the basis of computations required to match component velocity with overall saccade direction and amplitude. Although the data supporting these speculations are meager at present, such conjectures do form the basis of working hypotheses that can be tested experimentally. We also considered the implications of kinematic constraints, especially Donders' and Listing's laws, for future investigations. Tweed & Vilis (1987, 1990) proposed models specifically designed to handle these constraints. In their models, eye position is represented on four oculomotor channels: three coding the vector components of eye position, and one carrying a signal inversely related to gaze eccentricity and torsion. Yet, other evidence suggest that simpler computations may suffice for the implementation of laws that are only approximately obeyed.(ABSTRACT TRUNCATED AT 400 WORDS)