Observations of the millisecond pulsar B1937+214 at Nancay radioastronomy Observatory have yielded a very dense series with flux density and Time of Arrival measured about 10 times per month for several years at frequencies between 1.28 and 1.7 GHz. We have carried out a correlation analysis and found that the fluctuations of the flux density and time of arrival in this series have levels and time scales consistent with expectations based on the Kolmogorov model for the interstellar density spectrum. However, in the data, there is a sequence of about 5 discrete events, in which the flux remains low over 10-30 days and the Time of Arrival is on average late but also shows rapid variations. Assuming that these are indeed discrete events, we interpret them as due to isolated regions of enhanced plasma density crossing the line of sight. Such ``Extreme Scattering Events'' make a major contribution to the TOA variations that are anti-correlated with the observed flux. They are seen against a background of the normal refractive scintillation. A model is proposed in which discrete sheets of plasma cross the line of sight and cause a ``de-focussing'' event when aligned parallel to the line of sight. The statistics of the events imply a surprisingly large space density of the sheets; an alternative is that by chance we view PSRB1937+214 tangentially through a supernova shell which is fragmented and so causes multiple events.