A number of high-Tc superconducting cuprate phases related with YBCO were studied by means of high resolution electron microscopy and electron diffraction. The lower symmetry superstructures were widely detected. The superstructures are due to cation and/or oxygen atom ordering mainly in the MO1-x 'chain' layer, while the remaining part of the structure is hardly affected. The superlattice based on the 2 (root) 2ap X (root) 2ap X cp orthorhombic cell is found in the Co-1212 and Ga-12n2 compounds; a commensurate superstructure based on the 4ap X 2ap X cp orthorhombic cell in the Al-1222 compound, and an incommensurate modulated structure on the monoclinic cell 3.43ap X ap X 1.15cp in the S-1212 compound. A rock-salt layer ordering on the two-dim 2ap X 2ap superlattice was observed in the Ga-1222 compound; it appears as a consequence of partial replacement of Ba for Sr in the (Sr/Ba)O-GaO-(Sr/Ba)O lamella. A two-dim modulation in the CuO2 planes on a 2 (root) 2ap X 2 (root) 2ap superlattice was detected in the vacuum heated YBCO (Cu-1212), Al-1222, and Bi-2212 compounds. All these studies support the concept of cuprate superconductor structure as an alternating stack of MO-'chain' layers, whose structure determines the overall symmetry, and the CuO2-'block'-layers, which tends to preserve tetragonal symmetry regardless of the number of constituting perovskite, rock-salt, or fluoruite type layers.