1. Hurdle races: These are races where horses jump over a series of hurdles, which are smaller and more flexible than fences. Hurdle races are usually run over shorter distances than chase races.
2. Chase races: Also known as steeplechases, these are races where horses jump over larger and more solid fences. Chase races can be run over longer distances than hurdle races.
3. National Hunt Flat races: These are races for young horses that are run on a flat course without any obstacles. They are designed to introduce young horses to racing before they start jumping over hurdles or fences. (In ireland horses can revert to National Hunt Flat races after a run over hurdles but not in the UK)
4. Handicap races: As with flat racing, there are also handicap races in National Hunt racing, where the weight carried by each horse is determined by its ability to make the race more competitive.
5. Novice races: These are races for horses that have not won a certain number of races before. They are often restricted to a certain age group, and are designed to give younger horses experience before they move on to tougher races.
6. Grade 1, 2, and 3 races: Similar to flat racing, National Hunt races are also graded, with Grade 1 being the highest level of races. These races are often the most prestigious, and attract the best horses and jockeys.
7. Hunter chases: These are races for amateur riders and horses, where the horses must have previously run in a chase or hurdle race.

Each type of race provides different opportunities for trainers, jockeys, and horses, and they are all designed to test different skills and abilities. National Hunt racing is known for its thrilling jumps and exciting finishes, and is a popular spectator sport in the UK and Ireland.