A recent state-of-the-art neural open information extraction (OpenIE) system generates extractions iteratively, requiring repeated encoding of partial outputs. This comes at a significant computational cost. On the other hand,sequence labeling approaches for OpenIE are much faster, but worse in extraction quality. In this paper, we bridge this trade-off by presenting an iterative labeling-based system that establishes a new state of the art for OpenIE, while extracting 10x faster. This is achieved through a novel Iterative Grid Labeling (IGL) architecture, which treats OpenIE as a 2-D grid labeling task. We improve its performance further by applying coverage (soft) constraints on the grid at training time. Moreover, on observing that the best OpenIE systems falter at handling coordination structures, our OpenIE system also incorporates a new coordination analyzer built with the same IGL architecture. This IGL based coordination analyzer helps our OpenIE system handle complicated coordination structures, while also establishing a new state of the art on the task of coordination analysis, with a 12.3 pts improvement in F1 over previous analyzers. Our OpenIE system - OpenIE6 - beats the previous systems by as much as 4 pts in F1, while being much faster.