Tissue homeostasis relies on orchestrated multicellular circuits, where interactions between different cell types dynamically balance tissue function. While single-cell genomics identifies tissues' cellular components, deciphering their coordinated action remains a major challenge. Here, we tackle this problem through a new framework of multicellular programs: combinations of distinct cellular programs in different cell types that are coordinated together in the tissue, thus forming a higher order functional unit at the tissue, rather than only cell, level. We develop the open-access DIALOGUE algorithm to systematically uncover such multi-cellular programs not only from spatial data, but even from tissue dissociated and profiled as single cells, e.g., by single-cell RNA-Seq. Tested on spatial transcriptomes from the mouse hypothalamus, DIALOGUE recovered spatial information, predicted the properties of a cell's environment only based on its transcriptome, and identified multicellular programs that mark animal behavior. Applied to brain samples and colon biopsies profiled by scRNA-Seq, DIALOGUE identified multicellular configurations that mark Alzheimer's disease and ulcerative colitis (UC), including a program spanning five cell types that is predictive of response to anti-TNF therapy in UC patients and enriched for UC risk genes from GWAS, each acting in different cell types, but all cells acting in concert. Taken together, our study provides a novel conceptual and methodological framework to unravel multicellular regulation in health and disease.