  Subdiffusive motion of tracer particles in complex crowded environments, such
as biological cells, has been shown to be widepsread. This deviation from
brownian motion is usually characterized by a sublinear time dependence of the
mean square displacement (MSD). However, subdiffusive behavior can stem from
different microscopic scenarios, which can not be identified solely by the MSD
data. In this paper we present a theoretical framework which permits to
calculate analytically first-passage observables (mean first-passage times,
splitting probabilities and occupation times distributions) in disordered media
in any dimensions. This analysis is applied to two representative microscopic
models of subdiffusion: continuous-time random walks with heavy tailed waiting
times, and diffusion on fractals. Our results show that first-passage
observables provide tools to unambiguously discriminate between the two
possible microscopic scenarios of subdiffusion. Moreover we suggest experiments
based on first-passage observables which could help in determining the origin
of subdiffusion in complex media such as living cells, and discuss the
implications of anomalous transport to reaction kinetics in cells.
