Measured bioresponses are often characterized by an intrinsic high frequency and strong persistent correlations inhibiting statistical modeling by the traditional techniques. The talk overviews two novel wavelet-based techniques for modeling such challenging data. Wavelet domains provide natural modeling environments for data that scale, as well as for data consisting of continuous n-dimensional functions. We briefly discuss technicalities and describe in detail two applications. First application deals with wavelet analysis of functional ANOVA (FANOVA) where the observations are curves coming from clinical research. The second application discusses classification methods based on wavelet-based measures of irregular scaling (multifractal spectra) applied on high frequency pupillary responses for patients with various eye pathologies.