Since the early days of plasma physics research suprathermal electrons were observed to be generated during beam-plasma laboratory experiments. Energetic electrons, often modeled by $kappa$ distributions, are also ubiquitously observed in space. Various particle acceleration mechanisms have been proposed to explain such a feature, but all previous theories rely on either qualitative analytical method or on non-self-consistent approaches. This paper discusses the self-consistent acceleration of electrons to suprathermal energies by weak turbulence processes which involve the Langmuir/ion-sound turbulence and the beam-plasma interaction. It is discussed that the spontaneous scatttering process, which is absent in the purely collisionless theory, is singularly responsible for the generation of $kappa$ distributions. The conclusion is that purely collisionless Vlasov theory cannot produce suprathermal population.