The revolution in geometry, which has recently created the notion of t
he fractional dimension of real world bodies and has formed fractal ge
ometry, has substantially influenced fracture science. An experimental
ly measured crack in real materials has appeared to be substantially a
fractal, that is, a geometrical object of fractional dimension. In th
e present paper, an attempt has been undertaken to provide an account
of some achievements in this area, herein called ''Fractal Fracture Me
chanics''.