This paper presents a rigorous proof of the formation of extremal black holes on the threshold between gravitational collapse and dispersion. The authors construct smooth one-parameter families of spherically symmetric solutions to the Einstein–Maxwell–Vlasov system, which interpolate between dispersion and collapse. These solutions represent beams of self-interacting, collisionless charged particles fired into Minkowski space from past infinity. Depending on the parameter value, the Vlasov matter either disperses due to angular momentum and electromagnetic repulsion or undergoes gravitational collapse. At the critical value, an extremal Reissner–Nordström black hole is formed, with no naked singularities. This phenomenon is termed *extremal critical collapse*, and the paper provides the first rigorous result on the black hole formation threshold in general relativity. The authors also discuss the stability of extremal critical collapse and conjecture that there exists a codimension-one submanifold in moduli space consisting of asymptotically extremal black holes. Additionally, they explore the implications of this phenomenon for the third law of black hole thermodynamics and event horizon behavior at extremality.This paper presents a rigorous proof of the formation of extremal black holes on the threshold between gravitational collapse and dispersion. The authors construct smooth one-parameter families of spherically symmetric solutions to the Einstein–Maxwell–Vlasov system, which interpolate between dispersion and collapse. These solutions represent beams of self-interacting, collisionless charged particles fired into Minkowski space from past infinity. Depending on the parameter value, the Vlasov matter either disperses due to angular momentum and electromagnetic repulsion or undergoes gravitational collapse. At the critical value, an extremal Reissner–Nordström black hole is formed, with no naked singularities. This phenomenon is termed *extremal critical collapse*, and the paper provides the first rigorous result on the black hole formation threshold in general relativity. The authors also discuss the stability of extremal critical collapse and conjecture that there exists a codimension-one submanifold in moduli space consisting of asymptotically extremal black holes. Additionally, they explore the implications of this phenomenon for the third law of black hole thermodynamics and event horizon behavior at extremality.