We investigate optical absorption spectra and excitons in conjugated polyme
rs from first principles. This is done by calculating the one-particle and
the two-particle Green's function, including relevant many-body effects, an
d evaluating quasiparticle and optical excitations. Trans-polyacetylene and
poly phenylene-vinylene are studied as prototype long chain polymers. The
electron-hole interaction gives rise to large exciton binding energies (sim
ilar to 1 eV) and dramatically alters the optical spectra. The calculated e
xciton wave functions are very extended in real space.