  Period polynomials have long been fruitful tools for the study of values of
$L$-functions in the context of major outstanding conjectures. In this paper,
we survey some facets of this study from the perspective of Eichler cohomology.
We discuss ways to incorporate non-cuspidal modular forms and values of
derivatives of $L$-functions into the same framework. We further review
investigations of the location of zeros of the period polynomial as well as of
its analogue for $L$-derivatives.
