  We consider two aspects of the ground state of the $U=\infty$ Hubbard ladder:
ferromagnetism and the metal-insulator transition at quarter-filling. First, we
present rigorous results for the $U=\infty$ Hubbard ladder in the limit of the
large inter-chain hopping ($t_{\perp}/t\to\infty$). In this limit, the total
spin $S$ of the ground state is shown to be zero for the electron density $n\le
0.5$ and its maximum ($S=S_{max}$) for $n>0.5$. The charge gap at
quarter-filling is $2t_{\perp}$. We extend these results to finite
$t_{\perp}/t$ by means of the density-matrix renormalization group method. We
estimate the phase boundaries with respect to spontaneous magnetization and the
charge gap at quarter-filling for finite $t_{\perp}/t$. Applying the extended
Aharonov-Bohm method, we give numerical evidence that the critical ratio
$t_{\perp}/t$, above which the charge gap opens, is less than 0.001.
Ferromagnetism in the t-J ladder is briefly discussed.
