In the nineteen century, the famous Victorian anatomist Richard Owen diagnosed Dinosauria using three taxa: Megalosaurus, Iguanodon and Hylaeosaurus, on the basis of three main features: large size and terrestrial habits, upright posture and sacrum with five vertebrae (because the specimens were from all Late Jurassic and Cretaceous, he didn’t know that the first dinosaurs had three or fewer sacrals). This characteristics were more mammalian. He even speculated that dinosaur had four-chambered hearts and warm blood like mammals.
New fossil findings from Europe and particularly North America forced to a new interpretation about those gigantic animals. In 1887, Harry Govier Seeley summarised the works of Cope, Huxley and Marsh who already subdivided the group Dinosauria into various orders and suborders. However, he was the first to subdivide dinosaurs into Saurischians and the Ornithischians, based on the nature of their pelvic bones and joints. Based on these features, Seeley denied the monophyly of dinosaurs.
At the mid 20th century, the consensual views about Dinosauria were: first, the group was not monophyletic; second almost no Triassic ornithischians were recognised, so they were considered derived morphologically, which leads to the third point, the problem of the ‘‘origin of dinosaurs’’ usually was reduced to the problem of the ‘‘origin of Saurischia,’’ because theropods were regarded as the most primitive saurischians.
In 1968, Romer wrote that ‘‘Very probably the saurischians arose in mildly polyphyletic fashion from two or several pseudosuchian forms.’’
A great influence on the views about the dinosaur origins was Alan Charig. He was Curator of Amphibians, Reptiles and Birds at the British Museum (Natural History), now the Natural History Museum, in London for almost thirty years. Charig thought that the first dinosaurs were quadrupedal, not bipedal. He based this on the kinds of animals that he and his colleagues found in the early Triassic localities of eastern and South Africa. He thought that forms such as ‘‘Mandasuchus’’ were related to dinosaurs, but that they had a posture intermediate between a sprawling and upright gait that he called ‘‘semi-improved” or ‘‘semi-erect’’.
The discovery of Lagosuchus and Lagerpeton from the Middle Triassic of Argentina (Romer 1971, 1972; Bonaparte 1975) induced a change in the views of dinosaurs origins. Also from South America came a variety of new dinosaurs, including the basal dinosaurs Herrerasaurus and Ischisaurus from the Ischigualasto Formation, the basal sauropodomorphs Saturnalia, Panphagia, Chromogisaurus, and the theropods Guibasaurus and Zupaysaurus, but no ornithischians except a possible heterodontosaurid jaw fragment from Patagonia.
The 70s marked the beginning of the a profound shift in thinking on nearly all aspects of dinosaur evolution, biology and ecology. This process was called the dinosaur renaissance.
In 1974 Robert Bakker and Peter Galton, based on John Ostrom’s vision about Dinosauria, proposed, for perhaps the first time since 1842, that Dinosauria was indeed a monophyletic group and that it should be separated (along with birds) from other reptiles as a distinct ‘‘Class”.
Gauthier, in 1986, showed that Dinosauria was cladistically monophyletic and that birds were hierarchically included in Saurischia and Theropoda.

A meeting of vertebrate paleontologists (1968). From left to right: Romer, Bonaparte, W. Sill, R. Casamiquela, R. Pascual and O. Reig. (From F. Novas, 2009)
As pointed out by Steve Brusatte: “The evolutionary radiation of dinosaurs did not follow a simple pattern, but by the Early Jurassic, the Age of Dinosaur dominance was in full swing.”
References:
Padian K 2013. The problem of dinosaur origins: integrating three approaches to the rise of Dinosauria. Earth and Environmental Science Transactions of the Royal Society of Edinburgh, Available on CJO 2013 doi:10.1017/S1755691013000431