Compression methods have become of fundamental importance in almost every subfield of scientific visualization. However, unlike image compression, advanced visualization applications impose manifold constraints on the design of appropriate algorithms, where progressiveness, multiresolution or topology preservation are some of the key issues. This paper demonstrates the importance of multiresolution compression methods for visualization using two examples: The first, compression domain volume rendering, enables one to visualize volume data progressively and instantaneously from its compressed data format and has been designed for WWW and networked applications. The second one is a multiresolution compression and reconstruction method that allows for progressive coding, transmission and geometric reconstruction of surfaces and volumes. Both of the presented methods are the so-called transform coding schemes and use wavelets for data representation.