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Tensor products of vector spaces are fundamental objects in mathematics. The tensor product of two vector spaces can be studied using matrices, and this case is well-understood; the rank can be calculated easily, and equivalence corresponds precisely with rank. However for higher order tensors, problems such as calculating the rank or determining equivalence becomes very difficult. The case of the tensor product of three isomorphic vector spaces corresponds to algebras in which multiplication is not assumed to be associative. In this case, the tensor rank gives an important measure of the complexity of the multiplication in the corresponding algebra. For the case of a finite semifield (i.e. a not-necessarily associative division algebras), lower bounds can be obtained using results from linear codes, while for field extensions upper bounds can be obtained via polynomial interpolation and algebraic geometry. In this talk we will survey these problems and present new results where we determine the tensor rank of all finite semifields of order 81. In particular we show that some semifields of order 81 have lower tensor rank than the field of order 81, the first known example of such a phenomenon. This is joint work with Michel Lavrauw.