Shields in the 12th century were undergoing the transformation from the Norman long shields (also known as kite shields or tear drop shields) towards the rather iconic heater shield (the ones always used for coats of arms).
Focusing upon north Western Europe (purely because its the area i know most about):
Round shields are quite rare though they occasionally seem to have been used by cavalry archers in images (possibly referencing Arabic fighters or turcopoles). These seem to predominantly have been gripped by a web or straps (based upon rivet patterns and a common lack of a boss).
Militias and common foot soldiers seem to have used traditional long shields. Images show them bossed (the round mettle bulb in the centre) and un-bossed. This may be decorative or could indicate that some where "boss gripped" (i.e. by a bar which sits up the back of the shield, leaving the knuckles of the gripping hand inside the domed boss, as per the well known, older, Anglo-Saxon and Scandinavian shields). In images these long shields are shown gripped at a variety of angles.
Knights, and possibly other professional soldiers, during the 12th century seem to commonly use “flat topped” kite shields. These are of the same proportion as a “kite shield” but rather than curving to a smooth semicircular top they have squared off corners.
Finally some images of particularly wealthy individuals show smaller versions of these flat top shields sometimes known as “transitional kite shields” or “transitional heaters”. This has sometimes been ascribed to artistic licence (it is easier to make a fight look dynamic without a load of massive awkwardly shaped boards waving about through the image and blocking the view of the fighters and the gore). Others argue that with the development of cap-a-pie maille (literally “head-to-toe”) and face plate helmets that these smaller shields display a confidence in the armour of the wealthy and a need for increased mobility/ visibility while wearing it. This argument can be further supported by the sudden reappearance/popularity of two handed weapons in the 13th century.
Note: Numerous other shields appear in images dated to this period, though it is very difficult to establish if the image is a flight or fancy of some outside influence. Some soldiers are depicted with oval shields and in one image to duellists fight with small curved section square shields. There are many excuses for such oddities but it must be understood that they may have been about.