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To attempt to explain it in the simplest terms, a continuation is a representation, at a particular point in a program, of everything the program is capable of doing subsequently. A continuation is a potential that depends on initial conditions. Rather than loop in a traditional way, it is possible to invoke the same continuation recursively with different initial conditions. One broad claim I have read is that continuations, in a theoretical sense, are more fundamental and underlie every other control structure. Don't worry if these ideas cause your brain to melt; that is a normal reaction.