Significant advances have recently been made in the long-standing problem o
f light particle tunneling dynamics in condensed matter. This has been achi
eved for both charged and neutral particles: experiments using the muon spi
n relaxation techniques unambiguously show that both muons in metals and mu
onium atoms (light 'hydrogen' isotopes) in insulators reveal tunneling effe
cts at low temperatures. A major step forward has been made in studying the
mechanisms of quantum diffusion of these particles under the influence of
crystalline disorder. In particular, progress in recent years is connected
with the problem of particle localization at low temperatures in disordered
media. (C) 1999 Elsevier Science Ltd. All rights reserved.