Recent advances in the theory of complex symmetric operators are presented and related to current studies in non-Hermitian quantum mechanics. The main themes of the survey are: the structure of complex symmetric operators, C -selfadjoint extensions of C -symmetric unbounded operators, resolvent estimates, reality of spectrum, bases of C -orthonormal vectors and conjugate-linear symmetric operators. The main results are complemented by a variety of natural examples arising in field theory, quantum physics and complex variables.
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