Observations made using COBE, SCUBA, ISO and MAMBO have provided a reasonable working knowledge of both the intensity of the submm and far-infrared background radiation and the source counts of luminous high-redshift dusty galaxies. However, because there are uncertainties in the background intensity determinations, the samples of detected galaxies are small, and most importantly, their redshift ... [Show full abstract] distributions are very incomplete, details of the evolution of dusty galaxies remain unresolved. The next steps forward in the field will be the launches of SIRTF and ASTRO-F, the commissioning of SOFIA and new, more capable ground-based mm/submm-wave cameras - BOLOCAM, SHARC-II and SCUBA-II - the use of ultra-long duration balloon experiments, such as BLAST, the construction of ALMA and the arrival of FIRST, and ultimately the advent of space-borne far-infrared interferometers, such as SPECS. There are also exciting prospects for direct mm/submm-wave CO-line redshift surveys using wide-band spectrographs. Using these new facilities, the number of high-redshift dusty galaxies known will be increased dramatically. Spectroscopy using SIRTF, SOFIA and FIRST will probe the astrophysical processes within these sources in detail, hopefully addressing the open question of the fraction of the counts and background radiation that is generated by the formation of high-mass stars and by active galactic nuclei (AGNs). The spatial and spectral structure of distant dusty galaxies will finally be resolved in detail using ALMA and SPECS.