Heise method

The Heise method, invented by Ryan Heise, is a intuitive method which requires no algorithms. It uses extremely few moves, but it may be difficult to get fast times using this method.
Contents
Steps
 Create four 1x2x2 blocks (also called Heise blocks), making sure that one color appears on none of the blocks. This color will be the color of the last layer. Note that these blocks do not necessarily have to be paired together when they are built. One of these blocks should be just two centers and an edge.
 Pair up the 1x2x2 blocks, while simultaneously orienting the lastlayer edges. Note that you will now have all of F2L minus a corner/edge pair finished.
 Create two corneredge pairs, and then solve all of the edges and two corners. This is typically a very difficult step for beginners to solve.
 Solve the final three corners with a commutator.
Pros
This method is more efficient than any of the main three speedcubing methods, and therefore it's also very good for fewest moves solving. Because there are no algorithms at all, users of this method generally become very good at intuitive blockbuilding and develop a highlevel understanding of the cube.
Cons
Every turn has to be planned out because there are no algorithms, so fast turners will be disappointed. Some of the steps, especially the third step, can be very difficult to get used to, and beginning cubers might not understand enough cube theory to be able to use this method at all.
Strategies
Step 1
The first step is blockbuilding. Knowledge of F2L can help here, but it is important not to treat the step as just F2L minus a pair. If possible, you should try to plan the first two blocks during inspection. The second block will normally be the inner square, and it can help if the colours match the first block which will give a maximum range of possibilities for the third block. However, you should always be prepared to do things differently.
Step 2
Step 2 seeks to orient edge the upper edges while rotating the blocks into an F2L1 state. Although not compulsory, orienting the edges now makes step 3 easier.
Step 3
The third step is the hardest stage to master, particularly the "two pairs" approach which seeks to simultaneously solve the last 5 edges and 2 corners. Ryan Heise's advice is:
First, master solving the 5 edges on their own (ignoring the corners), which you can do using only RU moves (assuming the edges are already oriented). The last three moves will always be RU*R' with U* being one of U, U2 or U'. ... Then, you can try the same with two corners attached to two of the edges. You just try the same strategy as above, treating the corner/edge pairs as just elongated pieces that need to be kept intact. It is rarely possible to do this just using RU moves.[1]
Step 4
Step 4 is the 3corner solve. Ryan Heise explains the 'intuitive' approach using commutators.[2] Alternatively, there are Last Three Corners algorithm sets available.
Variants
Old Heise
Ryan Heise published an earlier version of his method in 2003/4. This early method used a different sequence of steps and made use of algorithms. The method averaged under 45 moves and was also a viable speedcubing method. The steps were:
 Create the four Heise blocks and join the blocks together (intuitive).
 Insert the remaining middle edge and simultaneously orient the top edges (Mostly intuitive).
 Insert the last corner on the bottom and simultaneously permute the top edges. 17 cases (or 28? including mirrors).
 Solve the Last Four Corners. 42 cases (or 84 including mirrors).
A notable proponent of this method was Andy Camann who adopted this method in 2004. He was able to achieve sub17second averages, which was close to his CFOP average.
Internet Archive links:
 Ryan Heise's 2004 page (broken applets)
 Andy Camann's Heise pages (broken images, but there are algorithms for step 3)
SpeedHeise
SpeedHeise is an algorithm set developed by Matt DiPalma. It seeks to systemize step 3 of the Heise method similar to ZZ. After step 2 the final F2L pair is created in the upper layer and fed to the FrontRight as in the Winter Variation. An algorithm from a 72algorithm set (or a 24algorithm simplified set) is then selected to solve all 4 LLedges and 1 LLcorner, leaving just the last three corners unsolved.
FLFL
The FLFL Method simplifies step 3 of Heise. It provides a few algorithms to separately solve the final bottom corner, leaving the Last Four Corners to solve.