  The recent observation of discrepancies in the muonic sector motivates
searches for the yet undiscovered atom true muonium $(\mu^+\mu^-)$. To leverage
potential experimental signals, precise theoretical calculations are required.
I will present the on-going work to compute higher-order corrections to the
hyperfine splitting and the Lamb shift. Further, possible detection in rare
meson decay experiments like REDTOP and using true muonium production to
constrain mesonic form factors will be discussed.
