Several ground motion conditions that are of little concern for conventional structures can be quite important for structures having natural periods longer than 1 s. Firstly, a large long‐period pulse of motion, due to the effect of rupture propagation (directivity), is observed in the direction normal to the fault at strong motion stations located close to the fault. The fault‐normal motions are about twice as large as the fault‐parallel motions for periods longer than about 1 s. The importance of this effect, especially in strike‐slip earthquakes, has probably been underestimated in existing ground motion attenuation relations because until very recently most of the near‐fault strong motion data from large earthquakes have come from thrust earthquakes, for which directivity effects are usually less pronounced. Near‐fault recordings of the 1971 San Fernando, 1979 Imperial Valley, 1989 Loma Prieta, and 1992 Landers, California, earthquakes show large directivity effects. We describe the systematic characteristics of the directivity effect derived from empirical analysis of recorded data and from synthetic seismogram modeling of these data. Secondly, the trapping and amplification of long period waves by sedimentary basins can generate amplitudes that are significantly larger than those calculated from simple ID models of site resonance. Using a ID model with a plane wave incident from below, it is not possible to trap energy in the near‐surface sediment layers. However, for 2D and 3D basin models, waves become trapped as they enter the thickening edge of a basin, and partially escape as they reach the thinning edge of the basin. We show evidence from both recorded data and synthetic seismogram modeling of the San Fernando and Loma Prieta earthquakes that the surface waves are confined to the basin and are not recorded at rock sites adjacent to the basin. This implies that the long period ground motion response at sites within these basins is not adequately represented by the conventional approach of vertically propagating an adjacent rock recording through a ID soil column.