  We discuss the implications of the recently reported $R_K$ and $R_{K^*}$
anomalies, the lepton flavor non-universality in the $B\to K\ell^+\ell^-$ and
$B\to K^*\ell^+\ell^-$. Using two sets of hadronic inputs of form factors, we
perform a fit of the new physics to the $R_K$ and $R_{K^*}$ data, and
significant new physics contributions are found. We suggest to study the lepton
flavor universality in a number of related rare $B, B_s, B_c$ and $\Lambda_b$
decay channels, and in particular we give the predictions for the $\mu$-to-$e$
ratios of decay widths with different polarizations of the final state
particles, and of the $b\to d\ell^+\ell^-$ processes which are presumably more
sensitive to the structure of the underlying new physics. With the new physics
contributions embedded in Wilson coefficients, we present theoretical
predictions for lepton flavor non-universality in these processes.
