Keyphrase extraction is the task of automatically selecting a small set of phrases that best describe a given free text document. Keyphrases can be used for indexing, searching, aggregating and summarizing text documents, serving many automatic as well as human-facing use cases. Existing supervised systems for keyphrase extraction require large amounts of labeled training data and generalize very poorly outside the domain of the training data. At the same time, unsupervised systems found in the literature have poor accuracy, and often do not generalize well, as they require the input document to belong to a larger corpus also given as input. Furthermore, both supervised and unsupervised methods are often too slow for real-time scenarios and suffer from over-generation. Addressing these drawbacks, in this paper, we introduce an unsupervised method for keyphrase extraction from single documents that leverages sentence embeddings. By selecting phrases whose semantic embeddings are close to the embeddings of the whole document, we are able to separate the best candidate phrases from the rest. We show that our embedding-based method is not only simpler, but also more effective than graph-based state of the art systems, achieving higher F-scores on standard datasets. Simplicity is a significant advantage, especially when processing large amounts of documents from the Web, resulting in considerable speed gains. Moreover, we describe how to increase coverage and diversity among the selected keyphrases by introducing an embedding-based maximal marginal relevance (MMR) for new phrases. A user study including over 200 votes showed that, although reducing the phrase semantic overlap leads to no gains in terms of F-score, our diversity enriched selection is preferred by humans.