We apply the layer-multiple-scattering method to study the optical properties of different plasmonic architectures; namely two- and three-dimensional periodic arrays of metallic nanocylinders and of metallodielectric nanosandwiches. These structures exhibit various types of collective plasmonic resonances, tunable over a broad spectral range from infrared to visible frequencies, which cause large enhancement of the local field and give rise to interesting phenomena that we discuss and provide a consistent interpretation of the underlying physics. We analyze extinction spectra of finite slabs of the structures under consideration and explain the different spectral features. In relation to optical metamaterials, we deduce effective electromagnetic parameters by the S-matrix retrieval procedure for single- and multi-layer slabs of periodic arrays of metallodielectric nanosandwiches and propose a method to resolve ambiguities in the determination of the effective refractive index, which become prominent for thick slabs, based on the complex band structure of the corresponding infinite crystal.