Real space studies of the interaction of the two-dimensional electron gas provided by metal surface states with localized scatterers are presented. The results involve electron scattering by steps and point defects (adsorbates) at Au(111) and Ag(111) surfaces. These scattering events lead, through interference, to an oscillatory local density of states (LDOS), which is imaged in maps of (dI/dV)/(I/V). (I/V). Analysis of the LDOS oscillations provides insights into the scattering phenomena involved. We show that the decay of the amplitude of the oscillations as a function of distance from the scatterer can be accounted for by a model that describes the loss of coherence as a result of the wave number (k(parallel-to)) spread of the states probed by the STM. This model also explains the energy dependence of the amplitude of the oscillations and provides a basis for comparing results from different metal surfaces. Analysis of the properties of the oscillations shows that at low k(parallel-to), steps act very much like hard walls isolating the surface states of different terraces. At high k(parallel-to), however, the barriers become permeable. The circular LDOS waves that surround individual adsorbates on the terraces can be used to obtain information on their nature and charge state. Finally, we show that when the size of a terrace is decreased to a few coherence lengths, as in the case of small metal islands, quantum size effects appear. State densities of confined ("particle in a box") states are revealed in the spectroscopic images.