  Ramanujan made many beautiful and elegant discoveries in his short life of 32
years, and one of them that has attracted the attention of several
mathematicians over the years is his intriguing formula for $\zeta(2n+1)$. To
be sure, Ramanujan's formula does not possess the elegance of Euler's formula
for $\zeta(2n)$, nor does it provide direct arithmetical information. But, one
of the goals of this survey is to convince readers that it is indeed a
remarkable formula. In particular, we discuss the history of Ramanujan's
formula, its connection to modular forms, as well as the remarkable properties
of the associated polynomials. We also indicate analogues, generalizations and
opportunities for further research.
