I am currently interested in studying the moments of zeta function (or L-function in general) which is the quantity: \begin{equation} I_k(T) = \int_{0}^T|\zeta(1/2+it)|^{2k}dt \end{equation} $\textbf{Question:}$ Are there any expository papers/book chapters that are not very technical and at the same time provide some historical perspective, motivation, current status of the problem and such?
So far, I have been only able to find that the problem is still open for $k\geq 3$. As for the historical perspective\motivation, the best sources I have found are the "Introduction" sections of some technical papers related to this topic.