As an atomically thin membrane, graphene is a highly flexible material, a property that provides the opportunity to use strain engineering to control its electronic properties. Wrinkled or rippled graphene, suspended or on a substrate, reveals inhomogeneous charge distributions originating from underlying strain fields. Scanning tunneling microscopy (STM) measurements on locally deformed samples demonstrated electron confinement with peculiar charge distributions that break sublattice symmetry. The phenomena that differentiate carbon atoms in each unit cell result in local valley currents with application in the field of valleytronics, i.e., the manipulation of the valley degree of freedom for electronic purposes. Our previous studies demonstrated that valley filtering properties highly depend on the type of deformation considered, suggesting the possibility of producing them by design. Motivated by these ideas, we analyzed the fate of charge distributions in models of graphene with several Gaussian-shaped out-of-plane deformations arranged in different geometries. These preliminary works revealed the emergence of moiré-like patterns with pockets of localized charges and naturally led us to consider periodic (global) arrays of deformations. These systems describe various experimental settings where graphene lies on top of specially designed substrates with arrays of deformations. Strains induced by such structures result in superlattice potentials that modify electron dynamics and become practical tools to engineer the band structure. By considering different strain configurations, we identify the conditions for the existence of flat bands in the electronic band structure that present maximal band-gap separation. The origin of these bands is traced back to the unique nature of electronic states that separate into ‘trivial’ isolated bound states and ‘percolating topological’ states. These two types of states coexist in different spatial regions with distinct lattice geometries and give rise to unique signatures when measured by local probes such as STM. Under applied external voltages, transport may occur via topological chiral states in bands with non-trivial Chern numbers that percolate through the sample.