The behavior of the infinite horizon Lorentz gas is characterized by the interplay of strongly chaotic dynamics and long flights. This is reflected in particular by the non-standard scaling in the limit theorem for the position of the billiard particle. In this talk, I would like to discuss recent results which naturally generalize the almost sure invariance principle and the law of iterated logarithm to this setting. This is joint work with Dalia Terhesiu.