ABC of N=8, d=1 supermultiplets

We construct a variety of off-shell $N=8,d=1$ supermultiplets with finite numbers of component fields as direct sums of properly constrained $N=4,d=1$ superfields. We also show how these multiplets can be described in $N=8,d=1$ superspace where the whole amount of supersymmetry is manifest. Some of these multiplets can be obtained by dimensional reduction {}from $N=2$ multiplets in $d=4$, whereas others cannot. We give examples of invariant superfield actions for the multiplets constructed, including $N=8$ superconformally invariant ones.