He is currently Professor at both the KTH in Stockholm and Imperial College London.
From 2001 to 2003 Laptev served as the President of the Swedish Mathematical Society.[1]
He is Editor-in-Chief of Acta Mathematica, Editor-in-Chief of Arkiv för Matematik, Deputy Chief Editor of the "Journal of Spectral Theory", Editor of the "Bulletin of Mathematical Sciences", Editor of "Problems in Mathematical Analysis", and Editor of "Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika".