(Also, it's open-source.)
To expand on this comment a bit - OSRM still uses Dijkstra, so if you understand that, you already basically understand what OSRM does.
What OSRM does in order to speed things up is optimize the graph structure - we still use Dijkstra, but the search completes in a handful of steps, rather than hundreds of thousands.
There are quite a few techniques like this. OSRM implements an approach called Contraction Hierarchies. We scan over the graph, inserting "shortcuts" that skip over nodes. As long as you follow a few basic rules, you can repeatably insert shortcuts all over the graph. This gives you a routing graph that is equivalent, but a Dijkstra search will typically complete in a handful of iterations.
We hope one day to implement several other speedup techniques - each has advantages/disadvantages, depending on what you want to do. Contraction Hierarchies lead to very fast queries (~5ms for a cross-the-US route), but the pre-processing time is very long (~6hrs on a beefy machine for the OSM planet). Any updates to the graph require complete re-processing (new/removed roads, adjusted road speeds, etc). Other techniques compromise search performance for a bit more flexibility - faster update times, query customization (i.e. "avoid highways").
It's a really fascinating corner of CS theory to work in, I really enjoy it :-)
This paper:
https://arxiv.org/pdf/1504.05140.pdf
"Route Planning in Transportation Networks" gives an excellent overview of current search speedup techniques. It's a bit hefty, but if you're interested in knowing what's the state of the art, this is a good place to start.
Could you elaborate on why the preprocessing time is long? I didn't study contraction hierarchies, but to me it seems that computing shortcuts in a planar graph is the perfect fit for a divide-and-conquer approach.
OR you can drop pins on the map.
I run bike routing for North America and Western Europe using a heavily customised instance of OSRM (based on OSM data, of course):
http://www.kevanahlquist.com/osm_pathfinding/
It shows how nodes are explored on the map with different search algorithms and the optimal path once the search is completed.
Also, immutability is great when you're juggling 1000s of lon/lat arrays.
