Morse theory has been an indispensable tool in the study of manifolds,
but its generalization to orbifolds has gone mostly undeveloped until
the past decade. I will discuss the basic definitions surrounding Morse
theory for orbifolds (particularly the index of an orbifold critical
point) and show some examples which convey the correspondence between
orbifold Morse functions and orbifold-handle decompositions.

A
particular emphasis will be placed on oriented 3-dimensional orbifolds,
where we will see a list of 20 distinct handle-types. I will provide a
Morse function for an orbifold-three-sphere whose singular locus is a
set of Borromean rings, and we will look at the corresponding handle
decomposition. This example has the property that the singular
orbifold-handle attachments will affect the orbifold structure without
altering the topology of the underlying space.