  Estimates of the branching ratios for B_{d,s}->J/psi eta and B_{d,s}->eta
l+l- are obtained by SU(3) relation to B_d->J/psi K and B_d->K l+l-,
respectively, as functions of the eta mixing parameter, theta_P. Based on these
estimates, a discussion of the prospects for HERA-B, CDF-II, and ATLAS on these
processes is given. The CP violation in B_{d,s}-> J/psi eta is analyzed in
depth and a method to extract the angle gamma of the unitarity triangle is
discussed. Finally, a possible method to constrain the Wilson coefficient
C_{10A} from measurements on semileptonic B decays such as B_d->J/psi K and
B_s->eta l+l- is proposed along with a discussion of the prospects for future
experiments and form factor calculations to reach the precision required for
this method to be interesting.
