Hilbert bases, Graver bases and toric Gröbner bases are at the heart of many problems arising in mathematics or in practice. In this talk we present the main functionality and the algorithmic theory behind the software package 4ti2. Furthermore, we present applications (theoretical and computational) from various mathematical fields such as toric algebra, integer programming or statistics. Within this workshop, this talk is accompanied by a tutorial on 4ti2 by Peter Malkin.