  Berry curvature physics and quantum geometric effects have been instrumental
in advancing topological condensed matter physics in recent decades. Although
Landau level-based flat bands and conventional 3D solids have been pivotal in
exploring rich topological phenomena, they are constrained by their limited
ability to undergo dynamic tuning. In stark contrast, moir\'e systems have
risen as a versatile platform for engineering bands and manipulating the
distribution of Berry curvature in momentum space. These moir\'e systems not
only harbor tunable topological bands, modifiable through a plethora of
parameters, but also provide unprecedented access to large length scales and
low energy scales. Furthermore, they offer unique opportunities stemming from
the symmetry-breaking mechanisms and electron correlations associated with the
underlying flat bands that are beyond the reach of conventional crystalline
solids. A diverse array of tools, encompassing quantum electron transport in
both linear and non-linear response regimes and optical excitation techniques,
provide direct avenues for investigating Berry physics. This review navigates
the evolving landscape of tunable moir\'e materials, highlighting recent
experimental breakthroughs in the field of topological physics. Additionally,
we delineate several challenges and offer insights into promising avenues for
future research.
