Shelah's main gap says, informally, that complete countable first-order theories split into a structure side and a nonstructure side. On the structure side, the classifiable theories have models in uncountable cardinals described by invariants arising from stable decomposition. On the nonstructure side, the non-classifiable theories satisfy precise spectrum theorems giving the maximum possible number of pairwise non-isomorphic models in the relevant uncountable cardinals.