This paper tackles the problem of semi-supervised video object segmentation, that is, segmenting an object in a sequence given its mask in the first frame. One of the main challenges in this scenario is the change of appearance of the objects of interest. Their semantics, on the other hand, do not vary. This paper investigates how to take advantage of such invariance via the introduction of a semantic prior that guides the appearance model. Specifically, given the segmentation mask of the first frame of a sequence, we estimate the semantics of the object of interest, and propagate that knowledge throughout the sequence to improve the results based on an appearance model. We present Semantically-Guided Video Object Segmentation (SGV), which improves results over previous state of the art on two different datasets using a variety of evaluation metrics, while running in half a second per frame.