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 datasets for testing and evaluating new techniques. In this paper we present a description and results from the first such Science Data Challenge (SDC1). Based on SKA MID continuum simulated observations and covering three frequencies (560MHz, 1400MHz and 9200MHz) at three depths (8h, 100h and 1000h), SDC1 asked participants to apply source detection, characterization and classification methods to simulated data. The challenge opened in November 2018, with nine teams submitting results by the deadline of April 2019. In this work we analyse the results for 8 of those teams, showcasing the variety of approaches that can be successfully used to find, characterise 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.