Energy and optical spectra of excitons against a background of incompressible quantum liquids (IQL's) are investigated by finite-size computations in a spherical geometry and by symmetry arguments based on the composite fermion theory. Properties of excitons are governed by the parameter h/l, where h is a separation between electron and hole confinement planes and l is a magnetic length. When h/l\ensuremath{\lesssim}1, the energy spectrum comprises a single exciton branch ${\mathit{L}}_{0}$ and a quasicontinuum above it. With increasing h/l a multiple-branch exciton spectrum develops. Different branches ${\mathit{L}}_{\mathit{m}}$ may be classified by the index m, which identifies the minimum angular momentum, ${\mathit{L}}_{\mathit{m}}$, of the ${\mathit{L}}_{\mathit{m}}$ branch. There are two types of branches. The branches of the first type are symmetrically compatible with a model of an exciton as a neutral entity consisting of a valence hole and several fractionally charged quasiparticles. All these anyon branches have m values exceeding some critical value (m\ensuremath{\ge}3 for the \ensuremath{\nu}=1/3 IQL), and they are generically related to some specific states from the low-energy sector of the electron subsystem, and drop down below the original ${\mathit{L}}_{0}$ branch with increasing h/l. Comparative investigation of the number-of-particle dependencies of the electron and exciton spectra shows that these properties survive in the macroscopic limit and establishes a connection between anyon branches and the basic low-energy physics of IQL's.The branches of the second type remain above ${\mathit{L}}_{0}$ and cannot be treated in terms of low-energy electronic excitations. We argue that the sphere-onto-plane projection rule for neutral composite particles has a form L-${\mathit{L}}_{\mathit{m}}$=kR, where k is the particle quasimomentum and R is the sphere radius. Since a plane rather than a sphere is the dynamical space of an exciton, this projection rule clarifies the physical meaning of the multiple-branch spectra and establishes the selection rules for optical transitions. In particular, it identifies ${\mathit{L}}_{\mathit{m}}$'s as internal angular momenta of the excitons belonging to different branches. Momentum dependencies of the probabilities of magnetoroton-assisted transitions suggest that magnetorotons of an \ensuremath{\nu}=1/3 IQL are ${\mathit{L}}_{2}$ quasiparticles. We also show that doublet emission spectra originating from zero- and single-magnetoroton transitions persist in a wide region of the parameter values.