The effect of the saddle-splay elastic constant K-24 on nematic direct
or-fields is a topic of fundamental interest for the elastic theory of
liquid crystals and plays a vital role in device applications where n
ematic liquid crystals are confined to a curved geometry. The first me
asurement of K-24 came more than sixty years after the pioneering work
of Oseen, who made first steps toward the elastic theory of liquid cr
ystals. Today the study of saddle-splay elasticity has become an impor
tant topic in liquid crystal physics. In this review we summarize the
various methods used to measure K-24 in curved geometries and present
the detailed theory behind the measurements.