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I will discuss supersymmetric Euclidean spacetime Ad* lattices and supersymmetry preserving deformations of Matrix model as non-perturbative regularization schemes for U(N) supersymmetric Yang-Mills theories with sixteen supercharges in d=1,2,3 and 4 dimensions. An intimately related construction is the twisted version of supersymmetric gauge theories, sometimes referred as topological twisting. There are intriguing relations between these constructions: Most importantly, the lattice point group symmetry is a subgroup of the twisted Lorentz group (and not the Lorentz group per se), and the exact supersymmetry of the lattice is a nilpotent fermionic spin-zero (and not a spinor) supersymmetry of the twisted version. The symmetries of the lattice greatly reduce or completely remove the need for any fine tuning in achieving the quantum continuum limit. I will finalize the discussion by pointing some open problems.

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