  Kinetic equations of Vlasov type are in widespread use as models in plasma
physics. A well known example is the Vlasov-Poisson system for collisionless,
unmagnetised plasma. In these notes, we discuss recent progress on the
quasineutral limit in which the Debye length of the plasma tends to zero, an
approximation widely assumed in applications. The models formally obtained from
Vlasov-Poisson systems in this limit can be seen as kinetic formulations of the
Euler equations. However, rigorous results on this limit typically require a
structural or strong regularity condition. Here we present recent results for a
variant of the Vlasov-Poisson system, modelling ions in a regime of massless
electrons. We discuss the quasineutral limit from this system to the kinetic
isothermal Euler system, in a setting with rough initial data. Then, we
consider the connection between the quasineutral limit and the problem of
deriving these models from particle systems. We begin by presenting a recent
result on the derivation of the Vlasov-Poisson system with massless electrons
from a system of extended charges. Finally, we discuss a combined limit in
which the kinetic isothermal Euler system is derived.
