This paper gives a gentle introduction to Turchin's supercompilation and its applications in metacomputation with an emphasis on recent developments. First, a complete supercompiler, including positive driving and generalization, is defined for a functional language and illustrated with examples. Then a taxonomy of related transformers is given and compared to the supercompiler. Finally, we put supercompilation into the larger perspective of metacomputation and consider three metacomputation tasks: specialization, composition, and inversion.
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