This paper reports observation of four kinds of luminescence quantum beats (QBs) in semiconductor quantum dots (QDs). QBs of Zeeman-split bright heavy-hole excitons under a longitudinal magnetic field and QBs coming from the electron spin Larmor precession under a transverse magnetic field were observed for strain-induced GaAs QDs. Another type of QB between bright and dark heavy-hole excitons was observed in neutralized self-assembled InP QDs in a tilted magnetic field. Trionic QBs were observed in negatively charged InP QDs possessing only one excess electron in the absence of the magnetic field. Analysis of QBs gives us fine energy splittings of exchange energy and Zeeman splittings of exciton, electron and hole with an accuracy of 10μeV despite the broad inhomogeneous linewidth of 20-50meV.