In this chapter we'll introduce the two most commonly used models. In the tf-idf model, an important baseline, the meaning of a word is defined by a simple function of the counts of nearby words. We will see that this method results in very long vectors that are sparse, i.e. mostly zeros (since most words simply never occur in the context of others). We'll introduce the word2vec model family for constructing short, dense vectors that have useful semantic properties. We'll also introduce the cosine, the standard way to use embeddings to compute semantic similarity, between two words, two sentences, or two documents, an important tool in practical applications like question answering, summarization, or automatic essay grading.