  Inspired by the ideas from topological field theory it is possible to rewrite
the supersymmetric charges of certain classes of extended supersymmetric
Yang--Mills (SYM) theories in such a way that they are compatible with the
discretization on a Euclidean spacetime lattice. Such theories are known as
maximally twisted SYM theories. In this review we discuss the construction and
some applications of such classes of theories. The one-loop perturbative
renormalization of the four-dimensional lattice ${\cal N}=4$ SYM is discussed
in particular. The lattice theories constructed using twisted approach play an
important role in investigating the thermal phases of strongly coupled SYM
theories and also the thermodynamic properties of their dual gravitational
theories.
