We consider random spanning trees of ladder graphs or lattices, as well as point processes in d-dimensional space. They serve as random environments for biased random walks or exclusion processes. We plan to investigate (1) the speed of the random walk as a function of the bias (2) the speed of the tagged particle in the exclusion process (3) limit laws for the position of the walker or tagged particle, respectively. For spanning trees of integer lattices, we plan to consider "outwards biased'' random walks and study the same questions. We further plan to investigate biased random walks on point processes, generalizing the one-dimensional results in earlier work by Faggionato, Gantert and Salvi to the multidimensional case.