The authors define a map from higher Chow groups to Deligne homology for smooth complex quasiprojective varieties on the level of complexes. They define the map by sending a cycle to some associated current, and this map gives an explicit description of the map \(c_{p, n}:\text{CH}^p(X, n) \rightarrow H^{2p-n}_{\mathcal{D}}(X, \mathbb Z(p))\) constructed by S. Bloch [in: Algebraic cycles and the Beilinson conjectures, Contemp. Math. 58, 65–79 (1986; Zbl 0605.14017)]. They also generalize the classical Abel-Jacobi map (Griffiths’ prescription) and the Borel/Beilinson/Goncharov regulator type maps to higher Chow groups. This paper is even more interesting to read while comparing their map with the morphic Abel-Jacobi map constructed by M. Walker [Compos. Math. 143, 909–944 (2007; Zbl 1187.14014)].