Sponge farming has been experimentally performed for more than 100 years, with early attempts mainly devoted for the supply of bath sponges and for ornamental purposes. During the last decades, sponge farming has been proposed to produce biomass specifically for those species from which many structurally diverse bioactive compounds were isolated, frequently present in a low concentration that limits their commercial production. This point is very important because it offers an environmental-friendly approach for the use of sponges as a source of natural compounds for pharmacological, cosmeceutical, and nutraceutical industries. In addition, sponges can have an ecological role as filter-feeding animals with a great significance in marine benthic communities. Thanks to their aquiferous system, they can filter large amounts of sea water, retaining up to 80% of suspended particles, resulting in a good system to bioremediate the marine environment from different contaminants. Remarkably, few attempts at integrating aquaculture systems were performed by combining the increase in sponge biomass and their use for bioremediation, showing impressive results and opening new possibilities in the aquaculture sector. This review concerns both in situ and lab-based aquaculture methods for the production of sponge biomass and for the sponge-related bioremediation of the marine environment focusing on microorganisms and contaminants (heavy metals, pesticides, microplastics, and others). Moreover, a first overview about integrated aquaculture combining biomass increase and bioremediation, as a challenging perspective for marine biotechnologies, is included.