Unusual ferroelectricity emerges in nanoscale Perovskite oxides owing to their characteristic structures, and it strongly interacts with mechanical stress/strain, namely, "multi-physics property". For systematic understanding, the ferroelectricity and multi-physics property in the nano-components are discussed in terms of their "macroscopic" component shape (e.g., films, wires, tubes and dots) and "inner" inhomogeneous structure (e.g., domain walls and grain boundaries), based on the first-principles density-functional theory calculations. Moreover, this paper also presents a remarkable interplayed effect of the macroscopic shape and the inner structure on the property through a theoretical investigation on polydomain PbTiO3 ultrathin films.