I will report on a work in common with R. Hardt from Rice University. We generalise the tools of homological integration developed by H. Federer and W.H. Fleming in their study of normal and integral currents. The generalisation both concerns the ambient metric space and the group of coefficients and encompasses previous work by W.H. Fleming, L. Ambrosio and B. Kirchheim, B. White, and U. Lang. We will insist on the modern point of view that emphasises the regularity of 0-dimensional slices with respect to its variable in the range space. We will discuss the classical theorems, mainly the rectifiability of flat G chains of finite mass with coefficients in a White group.