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In this talk we will give an introduction to the theory of nite semifields, first studied by L. E. Dickson in 1905. His motivation was purely algebraic: what happens if you drop the axiom of associativity for multiplication in the denition of a nite (skew) field? This question arose naturally, as it was shown that the axiom of commutativity for multiplication could be removed in the axiomatic denition of a finite field (Dickson-Wedderburn). Nowadays these (nonassociative) algebraic structures are called semifields, a notion introduced by Knuth. They turn up in various areas of mathematics, and play a key role in finite geometry. We will introduce the basics concepts, give some examples and first results in the theory of nite semifields, and conclude with some applications.