Using realistic models of hydrogenated amorphous silicon and density functional methods, we explore doping and transport with the most popular impurities: boron and phosphorous. We discuss conventional analogies of doping based upon shallow acceptors and donors in a crystalline matrix and highlight the limitations of such an approach. We show that B enters the network always with considerable strain, whereas P is much more "substitutional" in a tetrahedral site. We show that H is attracted to strained centers, especially for B, which increases the likelihood of H passivation effects on B impurities. We elucidate doping and nondoping static configurations in doped a-Si-H, and the role of H passivation as a partial explanation for the well-known low doping efficiency the material exhibits. We show that thermal fluctuations (that induce both network motion and H hopping) can also significantly impact conduction. We draw comparisons to experimental work.