After the fall of the Roman empire, their ideas were spread around the world by the Christian church. People started to adopt their architectural styles, and called it Romanesque, "in the manner of the Roman".
The thing the Romanesque architects did was they figured out how to make vaulted ceilings. This was a big deal because before, everything had to be kind of boxy. The horizontal beam went on the vertical support, and so on. The invention of the vault system allowed for angled ceilings and taller roofs. The massive stones were held up by a system of ribs and bays. The ribs deposited the weight on extremely thick walls designed to hold a lot of weight and the bays were the spaces in-between the ribs. The space between two sides of the church was called the nave.
The buildings of this period were decorated tastefully inside and out. The insides were generally decorated with murals from the bible or other religious document and statues. An interesting trait carried over from Romanesque architecture, and that was that they didnt finish the backs of sculptures. They didnt think their gods could go through things, so many Roman and Romanesque sculptures, the insides of walls, and other relatively hidden places, were left unfinished. In contrast, the Greeks believed that their gods were all knowing, and finished every part of the buildings.