  Non-perturbative lattice studies of QCD in the chiral thermodynamic regime,
where chiral symmetry is spontaneously broken, require to deal with almost
quark zero modes in a theoretically clean and computationally efficient way. We
discuss the basic features and some realistic tests of a formulation, known as
lattice tmQCD, that fulfills these requirements. Based on a talk given by R.
Frezzotti at the conference HEP2001 (Budapest, July 2001)
