Rational control of the structures of multifunctional materials allows us to tune the electronic structures and quantum states of matter, discover new physical properties, thus enable new applications. Non-centrosymmetry and chirality of 2D hybrid materials could be enabled at the monolayer and bulk crystal structure level by structural tuning and screw dislocations. We have shown how screw dislocations can influence the phase, layer stacking, and interlayer twisting of 2D materials (such as MX2) to lead to new properties and novel quantum phenomena due to moiré superlattices. Beyond the optoelectronic applications, two-dimensional (2D) hybrid halide perovskites are also promising for emerging spin-orbitronic applications due to the tunable structure chemistry and large spin-orbit coupling, which can lead to Rashba and/or Dresselhaus spin splitting. Chiral microplates of 2D perovskites with chiroptical properties can be produced via a screw dislocation growth mechanism. Our recent work focuses on exploiting the complex interplay between the organic spacer cations, the A-site cations, metal cations and dimensionality to produce a diverse library of structures and crystal symmetries. For example, A-cation tuning can lead to globally centrosymmetric bulk structures that contain non-centrosymmetric monolayers. Such local non-centrosymmetry can be unmasked via external perturbation leading to nonlinear optical properties and Rashbaspin splitting. Globally polar symmetry in quasi-2D perovskites can be enabled by incorporating spacer cations with molecular dipoles, leading to ferroelectricity and persistent spin texture. These rational design strategies to unlock and control non-centrosymmetry, chirality, and twist of 2D (hybrid)materials open up new nonlinear and chiral optical properties, spin-orbitronic, twistronics, and quantum applications.