We consider general second order boundary value problems on the whole line of the type $u^{\text{'}\text{'}}=h(t,u,u^{\text{'}})$, $u(-\infty )=0,u(+\infty )=1$, for which we provide existence, non-existence, multiplicity results. The solutions we find can be reviewed as heteroclinic orbits in the $(u,u^{\text{'}})$ plane dynamical system.