  We present the discovery observations for the optical counterpart of the
$\gamma$-ray burster GRB 970508 and discuss its light curve in the context of
the fireball model. We analyze the HST data for this object, and conclude that
any underlying galaxy must be fainter than $R$ = 25.5. We also present a
detailed analysis of the HST images of GRB 970228 claimed to show a proper
motion of the optical counterpart and conclude that, within the uncertainties,
there is no proper motion. We examine several aspects of the neutron-star
merger model for $\gamma$-ray bursts. In particular, we use this model to
predict the redshift distribution of $\gamma$-ray bursters, and adopting a
recent determination of the cosmic star-formation history, we show that the
predicted distribution of $\log N - \log P$ relation is consistent with that
observed for GRBs.
