Part One covers the New World, starting with a visit to a potato farmer in the Andes, where potatoes were originally domesticated. The background material here encompasses labour service obligations, the hacienda system and land reform, as well as the horrors of the Huancavelica mercury mine. The archaeological debate over the Clovis horizon and the first settlement of the Americas is relevant because the key Monte Verde site included some potato specimens. And potatoes played a key role in the Tiwanaku state and later the Inca empire. In contrast, the Spanish worked hard to import European plants and agriculture and didn't end up making that much use of the potato: "After all, the potato was peasant food, grown and consumed by people who were dying in their thousands."
Also covered here are the biology and evolution of the potato Solanum tuberosum tuberosum and its high-altitude subspecies S. tuberosum andigena (not to be confused with the sweet potato Ipomoea batatas). There is also a general overview of the history of domestication, and of agriculture more generally.
Part Two moves to Europe. Working as a kind of detective, Reader tries to track down the earliest introduction(s) of the potato. The Canary Islands and Antwerp feature prominently here, but "all versions of the story crediting Raleigh with a role founder on what can only be called a case of mistaken identity". The potato brought major changes to European agriculture and economics, but early attitudes to it were often negative. Adoption in many countries, notably in central Europe, was driven by war and the threat of foraging armies: unlike cereals, potatoes could be left in the ground to make requisitioning harder.
Three chapters cover the Irish Great Famine and its broader context, with background on Irish history and economy and politics, an account of the adoption of the potato and the demographic boom and dependence that followed, and a description of the crop failures and the famine itself. This also covers events in Britain: Engels and Smith and the political economy of Irish labour as well as Peel and the debates over the Corn Laws.
Part Three turns to potato science and the rest of the world. Early work focused on attempts to understand and find a protection against potato blight — which is a fungal infection, controllable with copper-based Bordeaux mixture. Important contributions were made in Britain by Redcliffe Salaman and, following the British Empire Potato Collecting Expedition of 1938-39, by Jack Hawkes, and in the Soviet Union by Vavilov (before he was purged by Lysenko). Reader also touches on potato breeding and describes a boom-and-bust around 1900, when investors were lured by rumours of varieties with amazing properties.
In Papua New Guinea potatoes were adopted only in the last quarter or so of the 20th century and potato blight also arrived late, in 2003; in New Zealand, the potato had a significant effect on Maori demographics, helping to offset the introduction of new diseases. The potato raises conflicts between indigenous ways of life and the benefit of global integration, with one key development the possibility of "true potato seed" which would allow seeding instead of planting with tubers. And with the help of large agribusiness China has come from the famine of the Great Leap Forward, where potatoes had a marginal role — they were not in state production targets, but were not used much as a famine food either — to being the world's largest potato producer.
As even this bare summary shows, The Untold History is pretty broad-ranging, with good global coverage and only a slight emphasis on the English-speaking world. The sentiment is generally pretty upbeat — Reader manages to put a more positive spin on the government response to the Irish famine than usual, for example — but he does raise the dangers of monoculture and the ways in which potatoes have risked being a "crop of poverty".
Note: The Untold History of the Potato was also published as Potato: A History of the Propitious Esculent.