Cellular information processing is carried out by complex biomolecular networks that are able to function reliably despite environmental noise and genetic mutations. The robustness and evolvability of biological systems is supported in part by neutral networks and neutral spaces that allow for the preservation of phenotype despite underlying genotypic variation. This talk will describe two such spaces. The first are sequence niches that emerge in the process of satisfying constraints needed to avoid crosstalk among sets of promiscuous and paralogous proteins. The second are highly anistropic, sloppy parameter spaces that arise in multiparameter models of biomolecular networks. Implications of the structure of these spaces for cellular information processing will be discussed.