His research is concerned with the mathematical analysis of numerical algorithms for nonlinear partial differential equations.

[4] He was an invited speaker at the International Congress of Mathematicians in Madrid in 2006[5] and was Chair of the Society for the Foundations of Computational Mathematics (2002–2005).

[6] Other honours include: Fellow of the Institute of Mathematics and its Applications (FIMA, 2007), Charlemagne Distinguished Lecture (2011), IMA Service Award (2011), Professor Hospitus Universitatis Carolinae Pragensis, Charles University in Prague (2012–), Distinguished Visiting Chair Professor Shanghai Jiao Tong University (2013), President, SIAM United Kingdom and Republic of Ireland Section (2013–2015), London Mathematical Society/New Zealand Mathematical Society Forder Lectureship (2015),[7] Aziz Lecture (2015), BIMOS Distinguished Lecture (2016), John von Neumann Lecture (2016),[8] Sibe Mardešić Lecture (2018),[9] London Mathematical Society Naylor Prize and Lectureship (2021).

[10] Since 2005 Süli has been co-Editor-in-Chief of the IMA Journal of Numerical Analysis[11] published by Oxford University Press.

He is a member of the Scientific Advisory Board of the Berlin Mathematics Research Center MATH+[12] and the Board of the Doctoral School for Mathematical and Physical Sciences for Advanced Materials and Technologies of the Scuola Superiore Meridionale at the University of Naples,[13] and was a member of the Scientific Steering Committee of the Isaac Newton Institute for Mathematical Sciences at the University of Cambridge (2011–2014), the Scientific Advisory Board of the Berlin Mathematical School (2016–2018), the Scientific Council of Société de Mathématiques Appliquées et Industrielles (SMAI) (2014–2020), the Scientific Committee of the Mathematisches Forschungsinstitut Oberwolfach (Mathematical Research Institute of Oberwolfach) (2013–2021), and the Scientific Advisory Board of the Archimedes Center for Modeling, Analysis and Computation at the University of Crete (2010–2014).