  In this paper, using compute-and-forward as an example, we provide an
overview of constructions of lattices from codes that possess the right
algebraic structures for harnessing interference. This includes Construction A,
Construction D, and Construction $\pi_A$ (previously called product
construction) recently proposed by the authors. We then discuss two
generalizations where the first one is a general construction of lattices named
Construction $\pi_D$ subsuming the above three constructions as special cases
and the second one is to go beyond principal ideal domains and build lattices
over algebraic integers.
