  We give an introduction to the valuation theoretical phenomenon of "defect",
also known as "ramification deficiency". We describe the role it plays in deep
open problems in positive characteristic: local uniformization (the local form
of resolution of singularities), the model theory of valued fields, the
structure theory of valued function fields. We give several examples of
algebraic extensions with non-trivial defect. We indicate why Artin-Schreier
defect extensions play a central role and describe a way to classify them.
Further, we give an overview of various results about the defect that help to
tame or avoid it, in particular "stability" theorems and theorems on "henselian
rationality", and show how they are applied. Finally, we include a list of open
problems.
