An ultrafast intense laser pulse drives coherent wakefields of relativistic amplitude with a high phase velocity robustly supported by the plasma. The structures of wakes and sheaths in plasma are contrasted. While the large amplitude of wakefields involves collective resonant oscillations of the eigenmode of the entire population of plasma electrons, the wake phase velocity ~c and ultrafast nature of the laser pulse introduce the wake stability and rigidity. When the phase velocity decreases, wakefields turn into sheaths, which are more suitable for ion acceleration. This short review reports on 4 decades of discoveries on laser plasma accelerators.