The growing ubiquity of algorithms in society raises a number of fundamental questions concerning governance of data, transparency of algorithms, legal and ethical frameworks for automated algorithmic decision-making and the societal impacts of algorithmic automation itself. This article, an introduction to the discussion meeting issue of the same title, gives an overview of current challenges and opportunities in these areas, through which accelerated technological progress leads to rapid and often unforeseen practical consequences. These consequences—ranging from the potential benefits to human health to unexpected impacts on civil society—are summarized here, and discussed in depth by other contributors to the discussion meeting issue. This article is part of a discussion meeting issue ‘The growing ubiquity of algorithms in society: implications, impacts and innovations'.