Three flavors of twisted invariants of knots
  The Alexander polynomial of a knot has been generalized in three different ways to give twisted invariants. The resulting invariants are usually referred to as twisted Alexander polynomials, higher-order Alexander polynomials and $L^2$-Alexander invariants of knots. We quickly recall the definitions and we summarize and compare some of their properties. We also report on work by the authors on $L^2$-Alexander torsions and we conclude the paper with several conjectures on $L^2$-Alexander torsions. 
J\'er\^ome Dubois, Stefan Friedl and Wolfgang L\"uck
math.GT