||Donaldson-Thomas (DT for short) invariant was conceived about 20 years ago as a holomorphic analogue of Casson's invariant for 3-manifolds and enumerate stable sheaves on a Calabi-Yau 3-fold when there are no strictly semistable sheaves. In this talk, I will discuss generalizations of the DT theory to the case where strictly semistable sheaves are allowed. After briefly discussing a motivic theory by Kontsevich-Soibelman, a combinatorial theory by Joyce-Song and a quiver theory by Davison-Meinhardt, I will talk about two new theories by Kirwan's partial desingularization, one from vanishing cycles functor and the other by semi-perfect obstruction theory. The latter approach also enables us to construct the virtual structure sheaf and K-theoretic DT invariants. Based on joint work with Jun Li and Michail Savvas.