The ENIGMA Consortium (http://enigma.usc.edu) is an international consortium of over 900 scientists studying 18 brain diseases using neuroimaging, genetics and clinical data to answer questions about the brain over the human lifespan. Started in 2009, the Consortium grew to 340 institutions spanning 35 countries. Its 37 working groups published the largest neuroimaging studies to date for 5 major disorders - major depression, bipolar disorder, schizophrenia, OCD, and ADHD. Additional working groups conduct global neuroimaging studies of PTSD, addiction, including substance use disorder, anxiety disorders, including panic disorder and generalized anxiety disorder, and neurodevelopmental disorders including autism spectrum disorders and 22q deletion syndrome. ENIGMA also coordinates worldwide studies of epilepsy, ataxia, stroke recovery, and Parkinson’s disease. Here we explain how these working groups analyze brain MRI, diffusion MRI, and resting state fMRI, and coordinate, hundreds of secondary projects relating brain metrics to cognition and behavior, and to common and rare genetic variation. ENIGMA’s Genomics Core conducts genome-wide association studies (GWAS), as well as CNV-based and epigenetic analysis of brain images. ENIGMA's first epigenome-wide study of brain measures points to loci where epigenetic variation may relate to brain metrics. ENIGMA’s GWAS of brain MRI, DTI and EEG measures show overlap in genetic determination for different imaging markers, and between imaging markers and schizophrenia, ADHD, Alzheimer's disease, and Parkinson's disease. ENIGMA also studies normal brain variation and left-right hemisphere laterality on an unprecedented scale (>20,000 brain MRIs); ENIGMA-Plasticity conducts the largest GWAS to date of longitudinal brain measures, to better understand genomic factors that affect brain changes over time.We summarize ENIGMA’s 3 areas of study – disease, imaging, and genetics - and how ENIGMA partners with the PGC and other consortia to relate imaging and genetic information in psychiatry. We highlight new mathematical opportunities that arise in genetic analyses of brain scans, including “image-wide genome-wide” searches, “connectome-wide genome-wide” searches, and genetic clustering of imaging traits and network metrics. We note the challenges faced in using machine learning methods on images worldwide - including deep learning and multilayer neural networks. We point to solutions that work well in consortium settings, such as private distributed computing. ENIGMA’s global analyses of 18 major diseases have led us to continually revise current thinking on imaging correlates of psychiatric illness, effect sizes of brain metrics in various diseases, and how these vary by sex, duration of illness, treatment, and with genetic risk. Cross-Disorder Working Groups now compare the neurobiology of diseases with overlapping characteristics, using MRI, GWAS, and diffusion imaging. We show comparisons of affective disorders to disorders of compulsivity/impulsivity, suggesting characteristic and distinct patterns on brain MRI and DTI. ENIGMA is beginning to show how brain diseases differ, interact, and relate in terms of the brain systems and circuits affected, revealing factors that modulate their emergence and progression in individuals and populations.