Around the end of the 19th century, along with Miklós Ybl and Frigyes Schulek, Steindl was the most significant architect within the lands of the Crown of Saint Stephen.

His most famous work, the Hungarian Parliament Building (Országház) in Budapest, is regarded as a symbol of the capital city.

Steindl graduated from the Technical University of Budapest and the Academy of Fine Arts Vienna.

He was elected honorary and corresponding member of the Royal Institute of British Architects in 1891 and was admitted to the Hungarian Academy of Sciences in 1898.

He is most famous for the Hungarian Parliament Building, an example of Gothic Revival architecture erected on the Pest bank of the Danube, but his other outstanding works include the St Elisabeth Church in Budapest as well as the reconstruction of the St Elisabeth Cathedral in Košice and the Hunyadi Castle.