This paper presents Mir-BFT, a robust Byzantine fault-tolerant (BFT) total order broadcast protocol aimed at maximizing throughput on wide-area networks (WANs), targeting deployments in decentralized networks, such as permissioned and Proof-of-Stake permissionless blockchain systems. Mir-BFT is the first BFT protocol that allows multiple leaders to propose request batches independently (i.e., parallel leaders), in a way that precludes request duplication attacks by malicious (Byzantine) clients, by rotating the assignment of a partitioned request hash space to leaders. As this mechanism removes a single-leader bandwidth bottleneck and exposes a computation bottleneck related to authenticating clients even on a WAN, our protocol further boosts throughput using a client signature verification sharding optimization. Our evaluation shows that Mir-BFT outperforms state-of-the-art and orders more than 60000 signed Bitcoin-sized (500-byte) transactions per second on a widely distributed 100 nodes, 1 Gbps WAN setup, with typical latencies of few seconds. We also evaluate Mir-BFT under different crash and Byzantine faults, demonstrating its performance robustness. Mir-BFT relies on classical BFT protocol constructs, which simplifies reasoning about its correctness. Specifically, Mir-BFT is a generalization of the celebrated and scrutinized PBFT protocol. In a nutshell, Mir-BFT follows PBFT "safety-wise", with changes needed to accommodate novel features restricted to PBFT liveness.