Introduction The constructions of $\mathcal L_p$-spaces Isomorphic properties of $(p,2)$--sums and the spaces $R^\alpha_p$ The isomorphic classification of $R^\alpha_p$, $\alpha <\omega_1$ Isomorphisms from $X_p\otimes X_p$ into $(p,2)$--sums Selection of bases in $X_p\otimes X_p$ $X_p\otimes X_p$-preserving operators on $X_p\otimes X_p$ Isomorphisms of $X_p\otimes X_p$ onto complemented subspaces of $(p,2)$--sums $X_p\otimes X_p$ is not in the scale $R^\alpha_p$, $\alpha < \omega_1$ Final remarks and open problems Bibliography.
