It is a famous result due to Riesz that every bounded linear functional $f$ on a Hilbert space $\mathcal{H}$ is of the form $f(x)=\langle x,z \rangle$ for a unique $z\in H$.

On p.188 of *Introductory Functional Analysis and Applications*, Erwin Kreyszig mentions that:

It is of practical importance to know the general form of bounded linear functionals on various spaces. ... For general Banach spaces such formulas and their derivation can sometimes be complicated.

Could someone give a brief statement of some results concerning the form of bounded linear functionals on Banach spaces? What might be some good resources to get an overview of results addressing this issue? Thanks!