The utility of terahertz time-domain spectroscopy (THz-TDS) for biomedical applications was only realized about two decades ago. Since then, biomedical research using THz-TDS has expanded rapidly because terahertz waves are (1) nonionizing,(2) highly sensitive to tissue hydration,(3) similar in size to skin appendages, and (4) contain absorption features of biomolecules. While terahertz waves have shown to be useful tools for clinical indications involving the skin and cornea, terahertz techniques have yet to achieve full clinical adoption. In this dissertation, I will first show the relationship between THz-TDS and biomedicine by modeling the wave propagation through biological tissue. Biological samples typically include some rough surfaces and granularity, so I will show a novel signal processing technique to mitigate the effects of granular scattering. Some biological tissues, like the cornea, have negligible levels of electromagnetic scattering, so I will show a method for utilizing THz-TDS for corneal disease by studying the water diffusion dynamics in a corneal phantom.