My scholarly work to date falls into three categories: spectral geometry, spectral graph theory, and discipline-based education research. Spectral geometry is the oldest and most developed branch of my work and so it is the focus of this article. After a brief discussion of the origin of spectral geometry, Sect. 6.2 carefully considers whether or not we can hear the length of a vibrating string. This problem provides a concrete example of the fundamental objects in classical spectral geometry: the Laplace operator, its eigenvalues, and eigenfunctions. Using the vibrating string as a stepping stone, the discussion moves to the spectrum of the Laplace operator on a Riemannian manifold. Questions asked by spectral geometers in this setting are described and two important results about the Laplace spectrum of a manifold are discussed. Section 6.3 introduces the Steklov operator and its spectrum, showcasing a few results concerning the Steklov spectral geometry of a manifold with boundary. The objects that are the focus of my work in spectral geometry, called orbifolds, are described in Sect. 6.4.1. After that my contributions to the study of the Laplace and Steklov geometry of orbifolds are discussed. Sections 6.2, 6.3, and 6.4.1 are written to be accessible to a student who is familiar with differential equations, multivariable calculus, and linear algebra, respectively. Sections 6.4.2 and 6.4.3 will be easier to read for those with some background in abstract algebra and point-set topology, respectively. The article concludes with a brief discussion of my work in spectral graph theory and education research, as well as some thoughts about the next steps in my research program.