In the field of economic history, the overlap is high, to the extent that the roles are deeply blurred both ways. Firstly, macroeconomists tend to do historical research because  you can't exactly breadboard an economy, the way to improve our understanding of what is happening now is by looking at what happened in the past. For example, Ben Bernake, Chair of the US's Federal Reserve (the US central bank) from 2006 to 2014, published an important paper on the macroeconomics of the Great Depression. Christina Romer is another famous macroeconomist who has [published extensively] in economic history, while Brad DeLong and Deirdre McCloskey straddle the boundary between economics and history even more comprehensively. More mundanely, I wrote an answer here a year ago on the Bretton Woods system that was basically taken from one of my macroeconomics lectures (I did check my sources both to confirm my memory and to get the details). 

To do macroeconomic research is to do history, basically. 

Secondly, historians in the economic history field have to know a fair bit of economics to do useful work. To give an uncontroversial example: everyone knows when someone sells something then someone else must have brought it. What an economics degree gives you is training in thinking of that - as part of training in general equilibrium analysis more generally. So, if someone states that an important cause of the British industrial revolution was money earned from selling sugar and tobacco, the well-trained economist immediately wonders what the European middle- and upper-classes would have purchased with their money if the sugar and tobacco wasn't available, Portuguese wine, perhaps, and if so would the Portuguese wine-sellers be more or less likely to invest in the technologies behind the industrial revolution. (There are trade-offs to spending time developing this reflex rather than others, e.g. I've noticed myself that I don't tend to think of things like political and military concerns, it's not that I deny that they exist, it's just that they don't tend to come to mind.) Another important tool for economic history research is GDP, either as calculated by national statistical offices (in modern times) or as estimated by economic historians for earlier periods. GDP (and GNP) was very much designed by economists, Simon Kuznets won the 1971 Nobel Memorial Prize in Economics in large part for his work on measuring national income.  

The London School of Economics summarises this as:

Economic history combines the skills of the economist and statistician with those of the historian, political scientist and sociologist.  The programme provides a broad training in social science research methods and their application to historical study, including the role of theory, evaluation, analysis and explanation, quantitative techniques and computing, the use of sources and presentational skills.

On the other hand, academia is growing ever more specialised, so there is often a shortage of interaction outside of economic history specifically.

You ask about recent crossovers/discoveries. A couple spring to mind. 

Firstly, Robert Fogel in 1962 published a hugely important book: Railroads in American Economic Growth. He set out to estimate how much the US would have grown by if railroads hadn't existed and came to the surprising conclusion that:

that the level of per capita income achieved by January 1, 1890 would have been reached by March 31, 1890, if railroads had never been invented   (Reportedly, this conclusion surprised Fogel himself, he had assumed that of course railways were vital, and had merely set out to estimate how vital they were, quantitatively). Fogel, along with his colleague Stanley Engerman, also published a book Time on the Cross that argued that slavery in the USA was econoimcally viable before the Civil War. 

Another important area of work in economic history has been changes in our understanding of the British economy before the industrial revolution (and of the industrial revolution itself), based on research carried out by a wide range of economists/economic historians. In the 18th/19th century it was thought that the medieval English economy was very different in operation to that of the British economy of the day (the word "capitalism" was coined in the 19th century to refer to the then-economic system). There was the widespread idea that it was a feudual economy, where most people weren't involved in markets, or wage labour, or other such capitalist ideas. Historians and economists thought that a major change causing the British Revolution was the enclosures of common land from the 17th to 18th centuries. 

Post-WWII economic research means that the medieval economy is now regarded as highly market-based and accounts of the Industrial Revolution talk more about a gradual change. To quote the economic historian Gregory Clark:

The more we learn about medieval England, the more careful and reflective the scholarship gets, the more prosaic does medieval economic life seem. The story of the medieval economy in some ways seems to be that there is no story.

Back in the bad old days, when the scholarship was less careful, the medieval economy was mysterious and exciting. Marxists, neo-Malthusians, Chayanovians, and other exotics debated vigorously their pet theories of a pre-capitalist economic world in a wild speculative romp. But little by little, as the archives have been systematically explored, and the hypotheses subject to more rigorous examination, medieval economic historians have been retreating from their exotic Eden back to a mundane world alarmingly like our own.

On the topic of enclosures specifically, in the 1970s Deidre McCloskey (then Donald) published important papers arguing that the old system of open fields was economically efficient and the economic historian Robert Allen published research in 1982 arguing that enclosures raised efficiency much less than previously thought, Robert Allen argued not at all, though Deirdre McCloskey argued for some of an increase, maybe 10-20%. 

These are hardly a complete listing of all the recent cross-overs, I've picked them because they do touch on a couple of areas that I think are important for our understanding of economic history - firstly how our intuitions as to what is important in an economy can be very misleading (Fogel's railways example) and secondly how doubtful the traditional story of economies developing in specific stages (e.g. feudualism to capitalism) is. 

Sources (not given in text)

   Bernanke, Ben S. “The Macroeconomics of the Great Depression: A Comparative Approach.” Journal of Money, Credit, and Banking 27 (1995): 1-28. https://fraser.stlouisfed.org/title/1169/item/2399

Allen, R. (1982). The Efficiency and Distributional Consequences of Eighteenth Century Enclosures. The Economic Journal, 92(368), 937-953. doi:10.2307/2232676, https://www.jstor.org/stable/2232676?seq=15#metadata_info_tab_contents