The recent observation of quantum oscillations in underdoped high-Tc superconductors, combined with their negative Hall coefficient at low temperature, reveals that the Fermi surface of hole-doped cuprates includes a small electron pocket. This strongly suggests that the large hole Fermi surface characteristic of the overdoped regime undergoes a reconstruction caused by the onset of some order which breaks translational symmetry. Here we consider the possibility that this order is stripe order, a form of charge / spin modulation observed most clearly in materials like Eu-doped and Nd-doped LSCO. In these materials, the onset of stripe order is indeed the cause of Fermi-surface reconstruction. We identify the critical doping where this reconstruction occurs and show that the temperature dependence of transport coefficients at that doping is typical of metals at a quantum critical point. We discuss how the pseudogap phase may be a fluctuating precursor of the stripe-ordered phase.