The 1990's witnessed an explosion of wavelet-based methods in the
field of image processing.  This paper will focus primarily on
wavelet-based image compression. We shall describe the connection
between wavelets and vision and how wavelet techniques provide
image compression algorithms that are clearly superior to the
present JPEG standard.  In particular the wavelet-based algorithms
known as SPIHT, ASWDR, and the new standard JPEG2000, will be
described and compared.  Our comparison will show that, in many
respects, ASWDR is the best algorithm.  Applications to denoising
will also be briefly referenced and pointers supplied to other 
references on wavelet-based image processing.