Theoretical estimates and experimental data indicate that the new high Tc Oxides have an extremely short coherence length, of the order of the size of the unit cell. In contrast with the formerly known superconductors, this short coherence length gives rise to a new behavior of the superconducting order parameter, including large thermodynamic fluctuations in the vicinity of Tc and a strongly enhanced sensitivity to local defects. In particular, the order parameter is strongly depressed at the boundaries, including external surfaces and internal planar defects such as twin boundaries. This depression is most pronounced at high temperatures where the coherence length becomes larger than the extrapolation length. The boundaries act effectively as pair breaker, leading to a smeared density of states, suppressed surface superconductivity, reduced critical densities and to the glassy behavior for which there is considerable experimental evidence. The latter may be understood as resulting from the existence of an irregular network of internal Josephson junctions located at twin boundaries or other planar defects. Recent experiments pointing out to a quantitative correlation between twin boundaries density and superconducting properties will be reviewed.