  We discuss the determination of the CKM angle $\alpha$ using the non-leptonic
two-body decays $B\to \pi\pi$, $B\to \rho\rho$ and $B\to \rho\pi$ using the
latest data available. We illustrate the methods used in each case and extract
the corresponding value of $\alpha$. Combining all these elements, we obtain
the following determination of $\alpha_{\rm dir}=( 86.2^{+4.4}_{-4.0}~~ \cup~~
178.4^{+3.9}_{-5.1})^\circ$. We assess the uncertainties associated to the
breakdown of the isospin hypothesis and the choice of statistical framework in
detail. We also determine the hadronic amplitudes (tree and penguin) describing
the QCD dynamics involved in these decays, briefly comparing our results with
theoretical expectations. For each observable of interest in the $B\to \pi\pi$,
$B\to \rho\rho$ and $B\to \rho\pi$ systems, we perform an indirect
determination based on the constraints from all the other observables available
and we discuss the compatibility between indirect and direct determinations.
Finally, we review the impact of future improved measurements on the
determination of $\alpha$.
