Equilibrium statistical physics holds true for an ergodic system which loses all local information of its initial condition under time evolution. In the last decade, a flurry of theoretical work has shown that ergodicity can be broken in an isolated, quantum many-body system even at high energies in the presence of disorder, a phenomena known as many-body localisation (MBL). The recent experimental observation of MBL in ultra-cold atoms has raised a plethora of intriguing questions.

In this talk I will throw some light on the effect of dimensionality on the properties of MBL. In one dimension, the strongly localized regime is described in terms of quasi-local integrals of motion, also known as l-bits. Based on this picture we develop an efficient tensor network method to evaluate the entire spectrum of fully many-body localised systems. I will also present the non-ergodic properties of eigenstates of infinite range quantum spin glass models governed by localisation on the infinite dimensional hypercube. On going away from the limiting cases of one and infinite dimensions, I will develop a refined phenomenology of MBL in terms of l*-bits which are only approximately conserved and discuss their experimental consequences.