Greek fire was a weapon invented by the Byzantine army. It was a chemical compound that would burn and burn. It was very difficult to extinguish, it would even stay alight on the surface of water This made it an excellent weapon against enemy ships.
The pendentive dome was invented by Byzantine architects. It allowed a dome to be placed on top of a square structure or base. This new design was used in many cathedrals and important buildings. One great example is the Hagia Sophia.
The cross in square was a new way to design the interior of churches, basilicas and cathedrals. It was laid out in a way that the base would be the shape of a cross. This is a very popular way of constructing religious buildings to this day.