1. Shidara, M., Kawano, K., Gomi, H. & Kawato, M. Inverse-dynamics model eye movement control by Purkinje cells in the cerebellum. Nature 365, 50–52 (1993).

2. Krauzlis, R. J. & Lisberger, S. G. SS responses of gaze velocity Purkinje cells in the floccular lobe of the monkey during the onset and offset of pursuit eye movements. J. Neurophysiol. 72, 2045–2050 (1994).

3. Dash, S., Catz, N., Dicke, P. W. & Thier, P. Encoding of smooth-pursuit eye movement initiation by a population of vermal Purkinje cells. Cereb. Cortex 22, 877–891 (2012).

4. Herzfeld, D. J., Kojima, Y., Soetedjo, R. & Shadmehr, R. Encoding of action by the Purkinje cells of the cerebellum. Nature 526, 439–442 (2015).

5. Roitman, A. V., Pasalar, S., Johnson, M. T. V. & Ebner, T. J. Position, direction of movement, and speed tuning of cerebellar Purkinje cells during circular manual tracking in monkey. J. Neurosci. 25, 9244–9257 (2005).

6. Hewitt, A. L., Popa, L. S., Pasalar, S., Hendrix, C. M. & Ebner, T. J. Representation of limb kinematics in Purkinje cell simple spike discharge is conserved across multiple tasks. J. Neurophysiol. 106, 2232–2247 (2011).

7. Medina, J. F. & Lisberger, S. G. Links from complex spikes to local plasticity and motor learning in the cerebellum of awake-behaving monkeys. Nat. Neurosci. 11, 1185–1192 (2008).

8. Yang, Y. & Lisberger, S. G. Role of plasticity at different sites across the time course of cerebellar motor learning. J. Neurosci. 34, 7077–7090 (2014).

9. Kimpo, R. R., Rinaldi, J. M., Kim, C. K., Payne, H. L. & Raymond, J. L. Gating of neural error signals during motor learning. eLife 3, e02076 (2014).

10. Fujita, H. & Sugihara, I. Branching patterns of olivocerebellar axons in relation to the compartmental organization of the cerebellum. Front. Neural Circuits 7, 3 (2013).

11. Marr, D. A theory of cerebellar cortex. J. Physiol. (Lond.) 202, 437–470 (1969).

12. Albus, J. S., Branch, D. T., Donald, C. & Perkel, H. A theory of cerebellar function. Math. Biosci. 10, 25–61 (1971).

13. Kitazawa, S., Kimura, T. & Yin, P.-B. Cerebellar complex spikes encode both destinations and errors in arm movements. Nature 392, 494–497 (1998).

14. Keating, J. G. & Thach, W. T. Nonclock behavior of inferior olive neurons: interspike interval of Purkinje cell complex spike discharge in the awake behaving monkey is random. J. Neurophysiol. 73, 1329–1340 (1995).

15. Ke, M. C., Guo, C. C. & Raymond, J. L. Elimination of climbing fiber instructive signals during motor learning. Nat. Neurosci. 12, 1171–1179 (2009).

16. Soetedjo, R., Kojima, Y. & Fuchs, A. F. Complex spike activity in the oculomotor vermis of the cerebellum: a vectorial error signal for saccade motor learning? J. Neurophysiol. 100, 1949–1966 (2008).

17. Ojakangas, C. L. & Ebner, T. J. Purkinje cell complex and simple spike changes during a voluntary arm movement learning task in the monkey. J. Neurophysiol. 68, 2222–2236 (1992).

18. Maruta, J., Hensbroek, R. A. & Simpson, J. I. Intraburst and interburst signaling by climbing fibers. J. Neurosci. 27, 11263–11270 (2007).

19. Mathy, A. et al. Encoding of oscillations by axonal bursts in inferior olive neurons. Neuron 62, 388–399 (2009).

20. Najafi, F., Giovannucci, A., Wang, S. S.-H. & Medina, J. F. Coding of stimulus strength via analog calcium signals in Purkinje cell dendrites of awake mice. eLife 3, e03663 (2014).

21. Yang, Y. & Lisberger, S. G. Purkinje-cell plasticity and cerebellar motor learning are graded by complex-spike duration. Nature 510, 529–532 (2014).

22. Yang, Y. & Lisberger, S.G. Modulation of complex-spike duration and probability during cerebellar motor learning in visually guided smooth-pursuit eye movements of monkeys. eNeuro https://doi.org/10.1523/ENEURO.0115–17.2017 (2017).

23. Suvrathan, A., Payne, H. L. & Raymond, J. L. Timing rules for synaptic plasticity matched to behavioral function. Neuron 92, 959–967 (2016).

24. Kojima, Y., Soetedjo, R. & Fuchs, A. F. Changes in simple spike activity of some Purkinje cells in the oculomotor vermis during saccade adaptation are appropriate to participate in motor learning. J. Neurosci. 30, 3715–3727 (2010).

25. Soetedjo, R. & Fuchs, A. F. Complex spike activity of purkinje cells in the oculomotor vermis during behavioral adaptation of monkey saccades. J. Neurosci. 26, 7741–7755 (2006).

26. Person, A. L. & Raman, I. M. Purkinje neuron synchrony elicits time-locked spiking in the cerebellar nuclei. Nature 481, 502–505 (2011).

27. De Zeeuw, C. I. et al. Spatiotemporal firing patterns in the cerebellum. Nat. Rev. Neurosci. 12, 327–344 (2011).

28. Heck, D. H., De Zeeuw, C. I., Jaeger, D., Khodakhah, K. & Person, A. L. The neuronal code(s) of the cerebellum. J. Neurosci. 33, 17603–17609 (2013).

29. Tang, T., Suh, C. Y., Blenkinsop, T. A. & Lang, E. J. Synchrony is key: complex spike inhibition of the deep cerebellar nuclei. Cerebellum 15, 10–13 (2016).

30. Helmchen, C. & Büttner, U. Saccade-related Purkinje cell activity in the oculomotor vermis during spontaneous eye movements in light and darkness. Exp. Brain Res. 103, 198–208 (1995).

31. Raghavan, R. T. & Lisberger, S. G. Responses of Purkinje cells in the oculomotor vermis of monkeys during smooth pursuit eye movements and saccades: comparison with floccular complex. J. Neurophysiol. 118, 986–1001 (2017).

32. Ishikawa, T. et al. Releasing dentate nucleus cells from Purkinje cell inhibition generates output from the cerebrocerebellum. PLoS One 9, e108774 (2014).

33. Mano, N. & Yamamoto, K. Simple-spike activity of cerebellar Purkinje cells related to visually guided wrist tracking movement in the monkey. J. Neurophysiol. 43, 713–728 (1980).

34. Catz, N., Dicke, P. W. & Thier, P. Cerebellar-dependent motor learning is based on pruning a Purkinje cell population response. Proc. Natl. Acad. Sci. USA 105, 7309–7314 (2008).

35. Georgopoulos, A. P., Schwartz, A. B. & Kettner, R. E. Neuronal population coding of movement direction. Science 233, 1416–1419 (1986).

36. Stavisky, S. D., Kao, J. C., Ryu, S. I. & Shenoy, K. V. Trial-by-trial motor cortical correlates of a rapidly adapting visuomotor internal model. J. Neurosci. 37, 1721–1732 (2017).

37. Scudder, C. A., Fuchs, A. F. & Langer, T. P. Characteristics and functional identification of saccadic inhibitory burst neurons in the alert monkey. J. Neurophysiol. 59, 1430–1454 (1988).

38. Strassman, A., Highstein, S. M. & McCrea, R. A. Anatomy and physiology of saccadic burst neurons in the alert squirrel monkey. II. Inhibitory burst neurons. J. Comp. Neurol. 249, 358–380 (1986).

39. Noda, H., Sugita, S. & Ikeda, Y. Afferent and efferent connections of the oculomotor region of the fastigial nucleus in the macaque monkey. J. Comp. Neurol. 302, 330–348 (1990).

40. Sugihara, I., Wu, H. & Shinoda, Y. Morphology of single olivocerebellar axons labeled with biotinylated dextran amine in the rat. J. Comp. Neurol. 414, 131–148 (1999).

41. Kojima, Y., Robinson, F. R. & Soetedjo, R. Cerebellar fastigial nucleus influence on ipsilateral abducens activity during saccades. J. Neurophysiol. 111, 1553–1563 (2014).

42. Dean, P. & Porrill, J. The cerebellum as an adaptive filter: a general model? Funct. Neurol. 25, 173–180 (2010).

43. Bengtsson, F. & Jörntell, H. Specific relationship between excitatory inputs and climbing fiber receptive fields in deep cerebellar nuclear neurons. PLoS One 9, e84616 (2014).

44. Thier, P., Dicke, P. W., Haas, R. & Barash, S. Encoding of movement time by populations of cerebellar Purkinje cells. Nature 405, 72–76 (2000).

45. Mauk, M. D. & Donegan, N. H. A model of Pavlovian eyelid conditioning based on the synaptic organization of the cerebellum. Learn. Mem. 4, 130–158 (1997).

46. Fuchs, A. F. & Robinson, D. A. A method for measuring horizontal and vertical eye movement chronically in the monkey. J. Appl. Physiol. 21, 1068–1070 (1966).