As semi-arid and salt-affected landscapes expand under climate change and land degradation, interest has increased in fast-growing woody biomass that can support both land rehabilitation and material production. Paulownia species and commercial hybrids are frequently promoted for these purposes because of their rapid juvenile growth, coppicing capacity, and lignocellulosic composition. Reported performance, however, varies substantially across genotypes, sites, and management regimes. This critical review evaluates the biological basis, establishment requirements, drought and salinity responses, wood and fiber properties, functional-material applications, and integrated biorefinery pathways of Paulownia spp. Field observations, controlled stress experiments, wood-characterization results, and laboratory processing studies are interpreted separately through a genotype × environment × management (G×E×M) framework. The specific synthesis is a proposed evidence chain from site and genotype through feedstock properties to end use: field evidence can inform plantation feasibility, whereas processing results establish candidate applications but cannot establish the advantages of stress-grown biomass without paired feedstock measurements. Field studies support substantial variation in growth with water supply, drainage, soil condition, and genotype, but available studies do not establish a universal drought or salinity threshold or a consistently abrupt response. Selected hybrids perform well in particular managed trials; comparative superiority across environments and lower invasion risk remain unverified for many clones. Low wood density constrains some structural and volumetric fuel applications, while laboratory fractionation and biochar studies show process feasibility under specified conditions, not industrial superiority or a demonstrated benefit of stress-grown feedstock. Paulownia is thus a management-dependent candidate for site-matched biomass production. This review distinguishes comparatively supported site and material constraints from hypotheses about genotype-specific stress limits and integrated biorefinery value. Field validation, genetically identified planting material, measured soil and water conditions, feedstock characterization, and comparative process assessment are required before regional or industrial recommendations can be made.