We present a thorough investigation of the vector leptoquark hypothesis for a combined explanation of the B-physics anomalies. We analyze this hypothesis from a twofold perspective, taking into account recent results from B-physics observables and high-p T searches. First, using a simplified model, we determine the general conditions for a successful lowenergy fit in presence of right-handed leptoquark couplings (neglected in previous analyses). Second, we show how these conditions, in particular a sizable 2-3 family mixing, can be achieved in a motivated ultraviolet completion. Our analysis reinforces the phenomenological success of the vector leptoquark hypothesis in addressing the anomalies, and its compatibility with motivated extensions of the Standard Model based on the idea of flavor non-universal gauge interactions. The implications of right-handed leptoquark couplings for a series of key low-energy observables, namely B s → τ τ and τ → µ lepton flavor violating processes, both in τ and in B decays, are discussed in detail. The role of the ultraviolet completion in precisely estimating other low-energy observables, most notably ∆F = 2 amplitudes, is also addressed. also [32,37]).We provide a detailed implementation of the U 1 leptoquark in a renormalizable model based on the (flavor non-universal) gauge group SU (4) 3 × SU (3) 1+2 × SU (2) L × U (1) , which in turn can be embedded in PS 3 [31]. In this context, we complement the simplified-model analysis by including oneloop contributions to low-energy observables (most notably ∆F = 2 amplitudes and dipole operators) which can be reliably computed only within a UV-complete framework.The paper is organized as follows. In Section 2 we present the simplified-model analysis: we introduce the Lagrangian describing the U 1 couplings to SM fermions, and analyze its low-energy limit. We discuss all the observables insensitive to the UV completion (Section 2.2), which are later used to fit low-energy data (Section 2.3). We finally comment on the high-p T constraints (Section 2.4).The UV-complete model is presented and discussed in Section 3: on the model-building side we pay particular attention to the flavor structure of the model (Section 3.2); on the phenomenological side we present complete expressions for the UV-dependent (loop-induced) observables, which were omitted in the low-energy fit (Section 3.3). The results are summarized in Section 4.