We introduce Fluid Annotation, an intuitive human-machine collaboration interface for annotating the class label and outline of every object and background region in an image. Fluid Annotation starts from the output of a strong neural network model, which the annotator can edit by correcting the labels of existing regions, adding new regions to cover missing objects, and removing incorrect regions. Fluid annotation has several attractive properties: (a) it is very efficient in terms of human annotation time; (b) it supports full images annotation in a single pass, as opposed to performing a series of small tasks in isolation, such as indicating the presence of objects, clicking on instances, or segmenting a single object known to be present. Fluid Annotation subsumes all these tasks in one unified interface. (c) it empowers the annotator to choose what to annotate and in which order. This enables to put human effort only on the errors the machine made, which helps using the annotation budget effectively. Through extensive experiments on the COCO+Stuff dataset, we demonstrate that Fluid Annotation leads to accurate annotations very efficiently, taking three times less annotation time than the popular LabelMe interface.