Collisions and chaos in the Boltzmann-Grad limit

I will review our current state of knowledge on the mathematical derivation of the Boltzmann equation from Newtonian systems. This problem has been the objective of intensive effort over recent years. I will focus on the size of correlations in the dilute gas and discuss some delicate aspects of the convergence in the kinetic limit. A statistical analysis of collisions via analytical tools provides new insights on the scale transition.