In the last fifteen years there has been a heated debate on exactly what is going on in Tarski's theory of logical consequence. Since Etchemendy's publications in the eighties, contributions by, among others, Sher, Ray, Gomez-Torrente, and Bays have provided a much more detailed picture of Tarski's seminal 1936 paper. However, this intense focus on the original publication has led to several disagreements with respect to important interpretative issues related to Tarski's contribution. One of the bones of contention, and the only one I will treat in the talk, concerns Tarski's notion of model, the key element of Tarski's famous definition of logical consequence.  I will argue that Tarski upheld  a fixed-domain conception of model in his 1936 paper and that he was still propounding it in 1939. Thus, the 1936 conception of logical consequence is both intensionally and extensionally different from the one which is nowadays commonly accepted.