Certain classes of supersymmetric Yang-Mills (SYM) theories including
the well known N=4 SYM, that takes part in the AdS/CFT correspondence,
can be formulated on the lattice using the techniques of exact lattice
supersymmetry. In this talk I will provide the construction of such
theories and describe how great ideas such as topological field theories,
Dirac-Kahler fermions, geometric discretization all come together to
create lattice SYM theories that are exact-supersymmetric, gauge-invariant
and doubler-free on the lattice. Then I move on to discuss the one-loop
renormalization of N=4 SYM on the lattice, restoration of the full set of
supersymmetries, sign problem in these theories and also lattice study of
finite temperature phase transitions in SYM theories and their connections
to some black hole solutions in dual supergravity theories.