Geocoding and Network Analysis (and bus maps I never figured out how to make)

I, like most people, have a GPS application on my phone, and when I need to find directions I put in the address and go.  Google Maps does the heavy lifting for me.  What exactly goes into finding an address though?  The process, in reference to GIS, is called geocoding, and it is used in conjunction with network analysis to plan optimal routes for applications in things like EMS and public transportation.

Geocoding addresses is tantamount to querying a database and spatially locating locations associated with house/building numbers, streets and zip codes.  The address locator itself is quite customizable though, and can be modified according to the format of the input addresses.  The Network Analyst extension in ArcGIS can then be used to create a map like the one above on the left- which depicts a route from an address (11 Yorkshire Drive) to another location.  The useful thing about the brown line and the numbered points in that map is that they are more than just graphics of a line and some dots- they are actually recognized by the program as an interconnected route and stops.  Several years ago I had a GIS position with county transit, and created bus maps.  I remember drawing lines and points on a map as graphics, and cursing my inability to get the lines and points to "recognize" one another as stops and routes.  Clearly this would have been the ideal solution for that problem.