Integration theory of Lie type algebras

I will survey the recent developments made in the integration theory with effective formulas of algebraic structures stronger or higher than Lie algebras. On the stronger side, one can integrate efficiently the pre-Lie algebras and admissible Lie algebras controlling the deformation theories of algebras over an operad and bialgebras over a properad respectively. On the higher side, I will describe how one can integration $L_\infty$-algebras into infinity-groupoids with closed formulas.