  We examine the properties of ditauonium, an exotic atom consisting of a pair
of opposite-sign $\tau$ leptons bound together by the quantum electrodynamics
(QED) interaction in a hydrogen-like state. The energy levels, decay modes and
associated partial widths, as well as total widths and lifetimes of the ortho-
and para-ditauonium states are calculated. Higher-order QED effects --
including Lamb shifts, hyperfine splitting structure, and partial decay widths
corrections -- are incorporated up to approximately
next-to-next-to-leading-order (NNLO) accuracy. Beyond the dominant diphoton and
difermion decays, the rates of rare decay channels -- including Dalitz,
radiative, triple-photon, double-Dalitz, four-fermion, and neutrinos final
states -- are determined.
