In this talk, I will discuss some disordered quantum systems beyond the mean-field regime. Last year (joint work with H.~T.~Yau), we studied the delocalization conjecture for one-dimensional random band matrices by developing the loop hierarchy method and its tree approximation. Later (joint work with S.~Dubova, F.~Yang, and H.~T.~Yau), we combine this framework with nested diagrammatic techniques previously used in high-dimensional ($d>7$) analyses to construct a unified approach capable of handling non-mean-field operators in low dimensions ($d\le 3$). Most recently (joint with J.~Fan and F.~Yang), we established delocalization for power-law random band matrices in the full regime of the decay exponent $\alpha>0$ of the variance profile. The key challenge is to address the interplay between the non-mean-field nature of the model and the slow decay of the variance profile.