A survey on tight Euclidean $t$-designs and tight relative $t$-designs in certain association schemes

It is known that there is a close analogy between the two relations "Euclidean $t$-designs vs. spherical $t$-designs" and "relative $t$-designs in binary Hamming association schemes vs. combinatorial $t$-designs." We first look at this analogy and survey the known results, putting emphasis on the study of tight relative $t$-designs in certain $Q$-polynomial association schemes. We then specifically study tight relative $2$-designs on two shells in binary Hamming association schemes $H(n,2)$ and Johnson association schemes $J(v,k)$. The purpose of this paper is to convince the reader that there is a rich theory even for these special cases and that the time is ripe to study tight relative $t$-designs more systematically for general $Q$-polynomial association schemes.