Particle dynamics at the level of the Langevin equation with hydrodynamics are analyzed for a system containing an immobile matrix or a background macrosolute. The first and second cumulants of the dynamic structure factor S(k,t) and of the incoherent dynamic structure factor Si(k,t) are obtained. Details of the time limits in which Langevin behavior goes over to diffusive (Smoluchowski) behavior are considered at length, including effects that may arise if times shorter than this limit are experimentally accessible. For a particle diffusion through a fixed matrix, to first order in time, D is renormalized by hydrodynamic interactions with the matrix, but the probe-matrix potential energy U does not play an explicit role in renormalizing D. In the absence of hydrodynamic probe-matrix interactions, the first cumulant of Si(k,t) for a probe particle diffusing amidst a fixed matrix is determined by the free diffusion coefficient of an isolated probe. U appears explicitly in expressions for the second cumulant of Si(k,t).