A study has been made of the Barkhausen pulses that occur during polarization reversal in single crystals of barium titanate. By both pulse counting and oscillographic techniques, the pulse shapes and in particular their heights and rise times have been studied as a function of the crystal thickness and the applied field strength. The pulse shape represents an initial rapid increase in the volume of the region switched followed by a slower relaxational type of growth, the latter being described by a time constant of 5 to 6 \ensuremath{\mu}sec. The pulse heights increase with the crystal thickness and linearly with the applied field while they are practically independent of temperature between room temperature and 94\ifmmode^\circ\else\textdegree\fi{}C. The relaxation time is essentially independent of the crystal thickness, of the applied field, and of the pulse height. The total number of pulses in a given crystal is independent of the field and temperature. In crystals 5\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}3}$ cm thick, the average volume corresponding to a pulse is ${10}^{\ensuremath{-}11}$ ${\mathrm{cm}}^{3}$ while the total volume represented by all the pulses is less than one percent of the crystal volume between the electrodes. Individual pulses occur quite independently of each other and of their surroundings.These observations are not consistent with the usual jerky domain-wall motion models for the generation of Barkhausen pulses. It is concluded that the eventual size and shape of the rapidly switching region represented by a Barkhausen pulse are mainly determined by the crystal thickness and the condition that the depolarizing field within the region must not exceed the applied field. This criterion is successful in accounting for some of the features of the pulses if the region is assumed to be spike-shaped and extending more or less through the crystal thickness, in particular, the average pulse size and its dependence on the field. These deductions suggest that the Barkhausen pulses could represent the nucleation and initial stages of growth of new spike-shaped domains extending along the $c$ axis and that the fixed number of pulses given by a crystal would then indicate a definite number of nucleating sites on the crystal surfaces. Under certain conditions a spike-shaped critical nucleus is consistent with the empirically determined nucleation probability factor, $\mathrm{exp}(\ensuremath{-}\frac{\ensuremath{\alpha}}{E})$, where $E$ is the applied field strength.To account for the polarization reversal in the remainder of the crystal it is presumed that, after their formation, the spikes expand radially (sideways) in all directions. By using this model the rate of polarization reversal as a function of time can be formulated, assuming that the radial wall velocity is proportional to the field and the nucleations occur randomly. Satisfactory agreement with experiment is obtained at low fields if it is assumed that the expanding domains stop short of overrunning adjacent nucleating sites. Relaxing this restriction for higher fields again leads to good agreement with experiment. Also, the observed dependence of the switching time and the maximum current on the applied field is predicted by using certain approximations.