Precursor phenomena are critical issues for martensitic transformations. In this article, we show recent progress in understanding precursor phenomena to the R-phase transformation, which is important for both fundamentals and applications. Structural modulation in the parent phase was intensively studied by means of detailed analyses of the weak diffuse scattering of electrons with the aid of recently developed energy-filtered transmission electron microscopy coupled with x-ray diffraction. A peculiar domain-like structure, which originates from static transverse atomic displacements in the parent phase, was discovered by virtue of these advanced methods. The characteristics of this structure (e.g., size, shape, and temperature-dependence), as well as its role in the subsequent R-phase transformation, are discussed.