In this thesis, I investigate the theories of existence of Gottlob Frege (1848–1925), Bertrand Russell (1872–1970) and Ludwig Wittgenstein (1889–1951), three of the founding figures of analytic philosophy. As to Frege and Russell, I challenge the common historical narrative according to which they developed and defended what is usually called the second-order theory of existence. This theory says, in short, that existence is a property that only properties of objects can have, rather than a property that objects can have. I argue that this standard narrative is historically inaccurate in several important and surprising ways. Frege did not hold a second-order theory of existence at all. His account of negative existentials—sentences of the form ‘X does not exist’ where what takes the place of ‘X’ is a singular term—has thus been misunderstood almost universally. Although it would be a mistake to classify Russell as a second-order theorist, he did develop (around 1918–1919) a theory that closely resembles the second-order theory of existence, which I discuss. But I first defend the traditional interpretation of his Principles of Mathematics (1903) according to which Russell was committed to an abundant ontology through his analysis of negative existentials. I then argue that in a transformative period in his thinking, namely the years 1910–1914, his position is unstable with respect to negative existentials in a way he never appears to have realised. As to the Wittgenstein of the Tractatus Logico-Philosophicus (1921), I argue that he can be interpreted in two ways depending on how one understands the Tractarian analysis of propositions involving definite descriptions. On one interpretation, Wittgenstein’s theory of existence is very similar to Russell’s, on the other his theory is radically different.