This paper provides a survey of the so called 'axiomatic price (and qu
antity) index theory'. Within this theory a price index is a function
of base period and comparison period prices and quantities, on which c
ertain requirements (axioms and/or tests) are imposed. The main conclu
sions are (a) the requirement of circularity implies that price indice
s cannot depend on base period or comparison period quantities; (b) th
e evidence for choosing the Fisher price index as the ultimate index i
s not conclusive; (c) the use of Laspeyres and Paasche indices in offi
cial statistical systems can be legitimized.