In any nonlocal model of a physical phenomenon, one has to decide the extent of the nonlocality. In peridynamics (PD), nonlocality is defined by the “horizon region”, with its radius (when taken as a circular disk in 2D, or a sphere in 3D), the PD horizon size. In certain cases, particular material length scales are prominent and measurable. For example, the size of inclusions in a matrix leads to specific wave scattering effects. Material properties (elastic moduli, fracture toughness) and loading conditions also lead to identifiable length scales. One can then select the PD horizon (and the PD kernel) of a homogenized model of heterogeneous material to be in the same range as that particular length scale. A more complex scenario is when several length scales are present in a material, and not all of them are easily quantifiable, or when they combine in some complex fashion. I will discuss the options for selecting a “proper” size for the peridynamic horizon for a particular model. While for generic isotropic and homogeneous elastic materials subject to homogeneous deformations one can select an arbitrary horizon size (the response will be the same, in the bulk), when deformations are not homogeneous, as they happen to be near holes or notches, the horizon has to be selected in relation to the dimensions of these geometrical details. When a material has such a multitude of holes that we have to “rename” it as a porous material, homogenization can be used to allow using a much larger horizon size than the minute size of the pores. In fracture problems, regular homogenization for such materials may not be able to capture the observed failure modes, and an “intermediately-homogenized” PD model may be needed to be able to predict fracture and damage in such material systems at a lower cost than models that represent the detailed, pore-level microstructure. Distinguishing experiments that create thresholds in terms of crack behavior can also be used to decide on the appropriate size of the peridynamic horizon. An example from thermally-induced fracture in glass will be shown. I will conclude with progress in speeding up peridynamic computations that use the fast convolution-based method (FCBM, see PeriFast codes on GitHub).