  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.
