Eva Kallin's lemma on polynomial convexity

We give a survey on the use of Eva Kallin's lemma. This lemma gives a condition on two polynomially convex sets in C-n under which their union is polynomially convex. This result has proved to be a useful tool in different areas of complex function theory of several variables, for instance in the study of polynomial convexity of the union of totally real surfaces, and in approximation problems in function algebras.