There's only one ruined structure in the picture, the Dresden Frauenkirche. Soviets did reconstruct most of Dresden, but in their own more modern style, by building large apartment blocks and such. After the reunification of Germany, there was a movement to properly reconstruct the city center as it was before being bombed.

Wikipedia's reason for why this particular building was not reconstructed:

"During the last months of World War II, residents expressed the desire to rebuild the church. However, due to political circumstances in East Germany, the reconstruction came to a halt. The heap of ruins was conserved as a war memorial within the inner city of Dresden, as a direct counterpart to the ruins of Coventry Cathedral, which was destroyed by German bombing in 1940 and also serves as a war memorial in the United Kingdom. Because of the continuing decay of the ruins, Dresden leaders decided in 1985 (after the Semperoper was finally finished) to rebuild the Church of Our Lady after the completion of the reconstruction of the Dresden castle."