SCA "heavy" combat is a simulation of 14th century tournament combat. It is not choreographed, and is carried out at full speed, with "reasonable force". This normally means hard enough that you will get a bruise if you only have padding on that area. The closest Eastern martial art might be Kendo, but we don't care about that perfect-strike bollacks, a kill is a kill right :-> Target areas are just about everything above the knees, although some places are considered "unchivilerous" to aim for; like the groin and neck.
Armour standards are strictly enforced, and no-one has ever died during SCA combat (can you say the same for your sport?!). Most people generally wear "partial plate" armour, that is plate arm and leg harness, with say a coat-of-plates around the body. The most common helm is a simple Basinet. The absolute minimum allowable armour is designed to stop any permenant damage, but expect some major brusing.
Weapons are constructed from Rattan cane, and shaped, covered in protective tape, and usually have basket-hilts or other hand protection added. There are various maximun lengths and weights imposed, and you are not allowed any entangling weapons (flails, whips etc). Sword and "heater" shield is by far the most common weapon form. Spears, glaives and two-handed swords are the most popular choices for wars, although some do fight tourneys with them too. "Florinetine" (using two swords at once), axes and maces go through local phases of intrest, but in general are rather rare.
Forms of combat range from one-on-one 
(me fighting the King of Caid, John, in my 2nd evolution
armour; me fighting in DW Crown Tourney), through to large field battles. It is
often advisable to practice on a "Pell" - an inanimate object which you can
practice blows on, click here on how to make one.
Click on the thumbnail pictures for the full-sized version:
Pennsic, an annual event in
Pennsylvania, USA, often has over 4,000 fighters on the field at once.
The Shieldwall, a great
defensive formation. These Roman guys look great!
Ballista, which fires one metre
"arrows". You know when you have been hit.
Killing from behind. Normally
only allowed in field battles, or melees. This is me infamously slaying Sir Aggro,
and Baron Thomas at Canterbury Faire 1996.
Melee's are multi-fighter combats,
usually with tourney rules.
Ildhafn fighters.
Bows and crossbows have rules which are also strictly enforced.
"Dying" is all part of the
fun.
Period fencing, or
"light" combat is a less physical form of combat. Cloaks, bucklers, and
off-hand weapons are often used in conjunction with standard rapiers, foils, and
schlargers.
