Context. NGC 6530 is a young cluster, with a complex morphology and star-formation history. We present a statistical study of its global properties, using a new, large list of candidate members down to masses of 0.2−0.4 M_⊙ and Gaia DR2 astrometry. Aims. We consider a larger sky region compared to previous studies, to investigate the entire cluster until its periphery, including any diffuse population all around the main cluster. We study the distribution of extinction and age across the different regions, and obtain constraints on the star-formation history. We also study the dynamics of cluster members. Methods. Cluster membership was determined on the basis of literature X-ray data, Hα emission, near-IR and UV excesses from the VPHAS+ and UKIDSS photometric surveys and published near-IR catalogs, and Gaia DR2 astrometry; moreover, we used a method for photometric selection of M-type pre-main-sequence cluster members, which we recently developed and used for other star-formation regions. The list of candidates includes nearly 3700 stars, of which we estimate approximately 2700 to be genuine NGC 6530 members. Results. Using Gaia parallaxes, the cluster distance is found to be 1325 pc, with errors of 0.5% (statistical) and 8.5% (systematic), in agreement with previous determinations. The cluster morphology and boundaries are established with great confidence, from the agreement between the subsamples of members selected using different criteria. There is no diffuse population of members around the cluster, but there are minor condensations of true members in addition to the two main groups in the cluster core and in the Hourglass nebula. Two such subgroups are spatially associated with the stars 7 Sgr (F2II-III) and HD 164536 (O7.5V). There is a definite pattern of sequential star formation across the cluster, within an age range from less than 0.5 Myr to ∼5 Myr. Extinction is spatially non-uniform, with part of the population still embedded or obscured by thick dust. The precise Gaia proper motion data indicate that the NGC 6530 parent cloud collided with the Galactic plane around 4 Myr ago, and we suggest that event as the trigger of the bulk of star formation in NGC 6530. The internal cluster dynamics is also partially resolved by the Gaia data, indicating expansion of the main cluster population with respect to its center.