  This chapter aims at emphasizing the crucial role of partial reactivity of a
catalytic surface or a target molecule in diffusion-controlled reactions. We
discuss various microscopic mechanisms that lead to imperfect reactions, the
Robin boundary condition accounting for eventual failed reaction events, and
the construction of the underlying stochastic process, the so-called partially
reflected Brownian motion. We show that the random path to the reaction event
can naturally be separated into the transport step toward the target, and the
exploration step near the target surface until reaction. While most studies are
focused exclusively on the transport step (describing perfect reactions), the
exploration step, consisting is an intricate combination of diffusion-mediated
jumps between boundary points, and its consequences for chemical reactions
remain poorly understood. We discuss the related mathematical difficulties and
recent achievements. In particular, we derive a general representation of the
propagator, show its relation to the Dirichlet-to-Neumann operator, and
illustrate its properties in the case of a flat surface.
