  In this article, we compile the work done by various mathematicians on the
topic of the fixed divisor of a polynomial. This article explains most of the
results concisely and is intended to be an exhaustive survey. We present the
results on fixed divisors in various algebraic settings as well as the
applications of fixed divisors to various algebraic and number theoretic
problems. The work is presented in an orderly fashion so as to start from the
simplest case of $\Z,$ progressively leading up to the case of Dedekind
domains. We also ask a few open questions according to their context, which may
give impetus to the reader to work further in this direction. We describe
various bounds for fixed divisors as well as the connection of fixed divisors
with different notions in the ring of integer-valued polynomials. Finally, we
suggest how the generalization of the ring of integer-valued polynomials in the
case of the ring of $n \times n$ matrices over $\Z$ (or Dedekind domain) could
lead to the generalization of fixed divisors in that setting.
