A chamber system is a particular type of edge-labeled graph. We discuss when such
chamber systems are or are not associated with a geometry, and when they are
buildings. Buildings can give rise to point-line geometries under constraints imposed
by how a line should behave with respect to the point-shadows of the other geometric
objects (Pasini). A recent theorem of Kasikova shows that Pasini’s choice is the
right one. So, in a general way, one has a procedure for getting point-line
geometries from buildings. In the other direction, we describe how a class of
point-line geometries with elementary local axioms (certain parapolar spaces)
successfully characterize many buildings and their homomorphic images. A
recent result of K. Thas makes this theory free of Tits’ classification of polar
spaces of rank three. One notes that parapolar spaces alone will not cover all
of the point-line geometries arising from buildings by the Pasini-Kasikova
construction, so the door is wide open for further research with points and
lines.
