Dielectric (DS), IR spectroscopy, and H-1 MAS NMR are employed in the study of ice/water confined in nanoporous alumina with pore diameters ranging from 400 nm down to 25 nm. Within nanoporous alumina there is a transformation from heterogeneous nucleation of hexagonal ice in the larger pores to homogeneous nucleation of cubic ice in the smaller pores. DS and IR show excellent agreement in the temperature interval and pore size dependence of the transformation. DS further revealed two dynamic processes under confinement. The "fast" and "slow" processes with an Arrhenius temperature dependence are attributed to ice and supercooled water relaxation, respectively. The main relaxation process of ice under confinement (slow process) has an activation energy of 44 +/- 2 kJ/mol. The latter is in agreement with the reported relaxation times and activation energy of cubic ice prepared following a completely different route (by pressure). H-1 MAS NMR provided new insight in the state of ice structures as well as of supercooled water. Under confinement, a layer of liquid-like water coexists with ice structures. In addition, both ice structures under confinement appear to be more ordered than bulk hexagonal ice. Supercooled water in the smaller pores is different from bulk water. It shows a shift of the signal toward higher chemical shift values which may suggest stronger hydrogen bonding between the water molecules or increasing interactions with the AAO walls.