Atomic interferometry was born recently, towards the end of the 1980s. Its
development has been extremely fast, new techniques being pioneered indepen
dently and almost simultaneously in different laboratories all over the wor
ld. Nowadays, these techniques have reached a high level of sophistication,
opening a wide area of fundamental and practical applications. In this pap
er the general architecture of interferometers in which matter waves are co
herently manipulated is described. Various realizations of atom and molecul
e interferometers are reported, together with the major results obtained wi
th each type of interferometer. Finally, new trends and perspectives are gi
ven. Whilst the techniques seem to be almost completely achieved, new devel
opments are coming up, such as the use of new and non-ordinary sources. For
thcoming applications are numerous. They deal with the most fundamental asp
ects of quantum mechanics, with the metrology of fundamental constants, wit
h the use of interferometers as very sensitive probes of external interacti
ons and inertial effects, with atomic nanolithography, etc.