Conventional Reconfigurable intelligent surfaces (RIS) for wireless communications have a local position-dependent (phase-gradient) scattering response on the surface. We consider more general RIS structures, called nonlocal (or redirective) RIS, that are capable of selectively manipulate the impinging waves depending on the incident angle. Redirective RIS have nonlocal wavefront-selective scattering behavior and can be implemented using multilayer arrays such as metalenses. We demonstrate that this more sophisticated type of surfaces has several advantages such as: lower overhead through coodebook-based reconfigurability, decoupled wave manipulations, and higher efficiency in multiuser scenarios via multifunctional operation. Additionally, redirective RIS architectures greatly benefit form the directional nature of wave propagation at high frequencies and can support integrated fronthaul and access (IFA) networks most efficiently. We also discuss the scalability and compactness issues and propose efficient nonlocal RIS architectures such as fractionated lens-based RIS and mirror-backed phase-masks structures that do not require additional control complexity and overhead while still offering better performance than conventional local RIS.