For decades, a kind of nanoscale microstructure, known as the premartensitic “tweed structure” or “mottled structure,” has been widely observed in various martensitic or ferroelastic materials prior to their martensitic transformation, but its origin has remained obscure. Recently, a similar nanoscale microstructure also has been reported in highly doped ferroelastic systems, but it does not change into martensite; instead, it undergoes a nanoscale freezing transition—“strain glass” transition—and is frozen into a nanodomained strain glass state. This article provides a concise review of the recent experimental and modeling/simulation effort that is leading to a unified understanding of both premartensitic tweed and strain glass. The discussion shows that the premartensitic tweed or strain glass is characterized by nano-sized quasistatic ferroelastic domains caused by the existence of random point defects or dopants in ferroelastic systems. The mechanisms behind the point-defect-induced nanostructures and glass phenomena will be reviewed, and their significance in ferroic functional materials will be discussed.