  Weighted Leavitt path algebras were introduced in 2013 by Roozbeh Hazrat.
These algebras generalise simultaneously the usual Leavitt path algebras and
William Leavitt's algebras $L(m,n)$. In this paper we try to give an overview
of what is known about the weighted Leavitt path algebras. We also prove some
new results (in particular on the graded K-theory of weighted Leavitt path
algebras) and mention open problems.
