I will present a new construction of compact G_2-orbifolds with ADE singularities due to F. Reidegeld (built on previous work of B. Acharya). The holonomy in these examples is not exactly G_2, but is large enough to describe realistic models of M-theory. Both the construction and the structure of the singularities rely on the lattice description of the moduli of hyperkahler structures on K3 surfaces. Time permitting, I will mention how it should fit in the context of string dualities and mirror symmetry.