  We introduce a hierarchy of split principles and show that it parallels the
hierarchy of large cardinals. In the typical case, a cardinal being large is
equivalent to the corresponding split principle failing. As examples, we show
how inaccessibility, weak compactness, subtlety, almost ineffability and
ineffability can be characterized. We also consider two-cardinal versions of
these principles. Some natural notions in the split hierarchy correspond to
apparently new large cardinal notions. Such split principles come with certain
ideals, and one of the split principles characterizing a version of $\kappa$
being $\lambda$-Shelah gives rise to a normal ideal on $\mathcal P_\kappa
\lambda$. We also investigate the splitting numbers and the ideals induced by
these split principles, and the relationship to partition relations.
