Korean BBQ is just a method of preparing many different dishes. The meat can be marinated or is served un-marinated. The meat is usually beef or pork, but sometimes chicken or even duck. 

Popular marinated variations with beef are: bulgogi (불고기), galbi (갈비) and jumulleok (주물럭). A marinated version with pork is called dwaeji bulgogi (돼지불고기), or spicy pork bulgogi. 

Un-marinated barbecued pork belly is called samgyeopsal (삼겹살) and among the many un-marinated beef versions, chadol bagi (차돌박이), thinly sliced brisket point, is quite amazing. 

Below are (most likely) pieces of Mokshim sal (목심살), which is a cut of pork, which comes close to the German "Schweinenacken".

The green leaf wraps are well known. You can spice the meat with pajeori (파절이) green onion salad, a raw piece of garlic, raw green pepper and ssamjang (쌈장) dipping sauce, which is basically a mix of doenjang and gochujang. 

Besides meat there is always a selection of mushrooms, sliced onion rings or vegetables to be grilled alongside the meat. You can use a grill pan where the fat drips away, or you can use a grill pan, which contains the fat. This allows you to fry cooked rice, soaking up the fatty juices of the meat.