This paper reports the concepts of the fractal and exciton percolation (random walk) and the most new results of the luminescence in fractal structures of organic compounds and proteins.We show that the energy transfer on fractal structures of organic compounds where the direct trapping depends on the fractal dimension

d

while the multistep trapping is given in terms of the spectral dimension

d

.Triplet-triplet exciton (neutral Frenkel triplet exciton) annihilation on percolation clusters produces a singlet exciton. On fractal spaces

the kinetic equation of the annihilation depends on the spectral dimension

d

. It is observed from experiment that dimensionality changes asymptoticly from

d

(fractal space) to dimension d (Euclidean space) with the change of local heterogeneity of the system.