Understanding the structure and dynamics of plant communities in water-limited systems often calls for the identification of ecosystem engineers--key species that modify the landscape, redistribute resources and facilitate the growth of other species. Shrubs are excellent examples; they self-organize to form patterns of mesic patches which provide habitats for herbaceous species. In this paper we present a mathematical model for studying ecosystem engineering by woody plant species in drylands. The model captures various feedbacks between biomass and water including water uptake by plants' roots and increased water infiltration at vegetation patches. Both the uptake and the infiltration feedbacks act as mechanisms for vegetation pattern formation, but have opposite effects on the water resource; the former depletes the soil-water content under a vegetation patch, whereas the latter acts to increase it. Varying the relative strength of the two feedbacks we find a trade-off between the engineering capacity of a plant species and its resilience to disturbances. We further identify two basic soil-water distributions associated with engineering at the single patch level, hump-shaped and ring-shaped, and discuss the niches they form for herbaceous species. Finally, we study how pattern transitions at the landscape level feedback to the single patch level by affecting engineering strength.