This thesis presents significant new observations of nuclear wobbling, and thus expands our understanding of nuclear triaxiality and its prevalence in the nuclear chart. Triaxial nuclear shapes are a very rare phenomena and their experimental identification often relies on two unique signatures – nuclear wobbling motion and chiral rotation. While nuclear chirality is a well-studied phenomenon, experimental observations of wobbling nuclei are rather limited. With the identification of ¹³⁵Pr and ¹⁸⁷Au as wobblers, this work establishes triaxiality to be a general...