We prove global well-posedness of the short-pulse equation with small
initial data in Sobolev space H^2. Our analysis relies on local well-posedness 
results of Schafer & Wayne (2004), the correspondence of the short-pulse 
equation to the sine-Gordon equation in characteristic coordinates, and a 
number of conserved quantities of the short-pulse equation. We also find 
sufficient conditions for the wave breaking to occur if the initial data have 
large H^2 norm. The analysis relies on the method of characteristics and it 
holds both on an infinite line and in a periodic domain. Numerical 
illustrations of the finite-time wave breaking are given for the periodic 
short-pulse equation.