Hodge theory is arguably the most successful subject of modern geometry. It was initiated by Hodge and Lefschetz but it really took of after Deligne and especially Griffiths and his school entered the field. It has had many applications — from rationality questions to Mirror Symmetry. Later nonabelian Hodge theory was introduced by Hitchin and Simpson.
The Nonabelian Hodge theory lead to many new applications and originated one of the most dominant fields in Mathematics — Geometric Langlands program.
P. Griffiths, R. Donagi, N. Hitchin, C. Simpson, J. Morgan, R. Bezrukavinkov, M. Kontsevich,
T. Pantev, L. Katzarkov, C. Rietsch