The four-dimensional nucleome (4DN) consortium studies the architecture of the genome and the nucleus in space and time. We summarize progress by the consortium and highlight the development of technologies for (1) mapping genome folding and identifying roles of nuclear components and bodies, proteins, and RNA, (2) characterizing nuclear organization with time or single-cell resolution, and (3) imaging of nuclear organization. With these tools, the consortium has provided over 2,000 public datasets. Integrative computational models based on these data are starting to reveal connections between genome structure and function. We then present a forward-looking perspective and outline current aims to (1) delineate dynamics of nuclear architecture at different timescales, from minutes to weeks as cells differentiate, in populations and in single cells, (2) characterize cis-determinants and trans-modulators of genome organization, (3) test functional consequences of changes in cis- and trans-regulators, and (4) develop predictive models of genome structure and function.