Béla Bollobás has made significant contributions to the mathematical field of combinatorics, with a particular focus on graph theory. Béla has influenced diverse areas such as random and extremal graphs, functional analysis, graph polynomials, percolation and isoperimetric inequalities.

His research highlights include his work on phase transitions in the evolution of random graphs. He also introduced the Bollobás–Riordan ribbon polynomial and made contributions to the development of a general model for heterogeneous sparse random graphs. In addition, Béla is the author of a number of popular and definitive textbooks on varied mathematical subjects.

Béla has received many accolades in recognition of his work, including the Senior Whitehead Prize of the London Mathematical Society in 2007. As well as being a Fellow of the Royal Society, he has also been elected as an External Member of the Hungarian Academy of Sciences and as a Fellow of the American Mathematical Society.