Deep generative models, like GANs, have considerably improved the state of the art in image synthesis, and are able to generate near photo-realistic images in structured domains such as human faces. Based on this success, recent work on image editing proceeds by projecting images to the GAN latent space and manipulating the latent vector. However, these approaches are limited in that only images from a narrow domain can be transformed, and with only a limited number of editing operations. We propose FlexIT, a novel method which can take any input image and a user-defined text instruction for editing. Our method achieves flexible and natural editing, pushing the limits of semantic image translation. First, FlexIT combines the input image and text into a single target point in the CLIP multimodal embedding space. Via the latent space of an autoencoder, we iteratively transform the input image toward the target point, ensuring coherence and quality with a variety of novel regularization terms. We propose an evaluation protocol for semantic image translation, and thoroughly evaluate our method on ImageNet. Code will be available at https://github.com/facebookresearch/SemanticImageTranslation/