We consider the semilinear parabolic equation
 $$  u_t=u_{xx}+f(u),\quad x\in \mathbb R,t>0,   $$
where  $f$ is a bistable nonlinearity. It is well-known that for a large class of initial data, the corresponding solutions converge to traveling fronts. We give a new proof of this classical result as well as some generalizations. Our proof uses a geometric method, which makes use of spatial trajectories $\{(u(x,t),u_x(x,t)): x\in \mathbb R\}$  of the solutions.