In this talk we will discuss relations between completely invariant sets and renormalizations of expanding Lorenz maps, that is maps $f\colon [0,1]\to [0,1]$ satisfying the following three conditions:

1. there is a critical point $c\in (0,1)$ such that $f$ is continuous and strictly increasing on $[0,c)$ and $(c,1]$;

2. $\lim_{x\to c^{-}}f(x)=1$ and $\lim_{x\to c^{+}}f(x)=0$;

3. $f$ is differentiable for all points not belonging to a finite set $F\subseteq [0,1]$ and $\inf_{x\not\in F} f’(x)>1$;

with special emphasis on piecewise linear case.

The talk is based on joint works with L. Cholewa.