Salinity of the soil is highly detrimental to plant growth. Plants respond by a redistribution of root mass between main and lateral roots, yet the genetic machinery underlying this process is still largely unknown. Here, we describe the natural variation among 347 Arabidopsis thaliana accessions in root system architecture (RSA) and identify the traits with highest natural variation in their response to salt. Salt-induced changes in RSA were associated with 100 genetic loci using genome-wide association studies. Two candidate loci associated with lateral root development were validated and further investigated. Changes in CYP79B2 expression in salt stress positively correlated with lateral root development in accessions, and cyp79b2 cyp79b3 double mutants developed fewer and shorter lateral roots under salt stress, but not in control conditions. By contrast, high HKT1 expression in the root repressed lateral root development, which could be partially rescued by addition of potassium. The collected data and multivariate analysis of multiple RSA traits, available through the Salt_NV_Root App, capture root responses to salinity. Together, our results provide a better understanding of effective RSA remodeling responses, and the genetic components involved, for plant performance in stress conditions.