Quasi-wavelets (QWs) are particle-like entities similar to customary wavelets in that they are based on translations and dilations of a spatially localized parent function. The positions and orientations are, however, normally taken to be random. Random fields such as turbulence may be usefully represented as ensembles of QWs with appropriately selected size distributions, number densities, and amplitudes. This paper provides an overview of previous results concerning QWs. The points of emphasis are the following. (1) Self-similar ensembles of QWs with rotation rates scaling according to Kolmogorov's hypotheses naturally produce classical inertial-subrange and von Karman-like spectra. (2) The spatially localized nature of QWs can be advantageous in wave-scattering calculations and other applications. The scattered wavefield from a single QW can be readily derived and then integrated over scale and volume to obtain expressions for the total scattering cross section. (3) Anistropy, and momentum and heat transfer, in surface-layer turbulence can be described by introducing preferred orientations and correlations among QWs representing temperature and velocity perturbations. (4) Unlike Fourier modes, QWs can be naturally arranged in a spatially intermittent manner. Models for both local (intrinsic) and global intermittency are described.