The challenge targeted difficult automatic prediction problems of great societal and medical relevance, namely, the detection of Alzheimer's Dementia (AD) and the estimation of cognitive test scoress. Participants were invited to create models for assessment of cognitive function based on spontaneous speech data. Most of these models employed signal processing and machine learning methods. The ADReSS-M challenge was designed to assess the extent to which predictive models built based on speech in one language generalise to another language. The language data compiled and made available for ADReSS-M comprised English, for model training, and Greek, for model testing and validation. To the best of our knowledge no previous shared research task investigated acoustic features of the speech signal or linguistic characteristics in the context of multilingual AD detection. This paper describes the context of the ADReSS-M challenge, its data sets, its predictive tasks, the evaluation methodology we employed, our baseline models and results, and the top five submissions. The paper concludes with a summary discussion of the ADReSS-M results, and our critical assessment of the future outlook in this field.