As the largest radio telescope in the world, the Square Kilometre Array (SKA) will lead the next generation of radio astronomy. The feats of engineering required to construct the telescope array will be matched only by the techniques developed to exploit the rich scientific value of the data. To drive forward the development of efficient and accurate analysis methods, we are designing a series of data challenges that will provide the scientific community with high-quality data sets for testing and evaluating new techniques. In this paper, we present a description and results from the first such Science Data Challenge 1 (SDC1). Based on SKA MID continuum simulated observations and covering three frequencies (560, 1400, and 9200 MHz) at three depths (8, 100, and 1000 h), SDC1 asked participants to apply source detection, characterization, and classification methods to simulated data. The challenge opened in 2018 November, with nine teams submitting results by the deadline of 2019 April. In this work, we analyse the results for eight of those teams, showcasing the variety of approaches that can be successfully used to find, characterize, and classify sources in a deep, crowded field. The results also demonstrate the importance of building domain knowledge and expertise on this kind of analysis to obtain the best performance. As high-resolution observations begin revealing the true complexity of the sky, one of the outstanding challenges emerging from this analysis is the ability to deal with highly resolved and complex sources as effectively as the unresolved source population.