Here’s an article from The Telegraph summarizing the effectiveness of biochar. Very enlightening. In summary, yield is improved by 10+% in the first and second year but not third and forth year. The alkaline nature of biochar needs to be addressed.
There are probably enough studies on biochar now to draw some general conclusions. It looks like biochar improves the moisture-holding capacity of soils that are deficient in that respect, and often (but not always, depending on its pH) raises the pH of acid soils. Of course, gardeners have dealt with both those problems in other ways, by applying lime, making their own compost and sometimes by importing organic matter. All of which are highly effective, and probably cheaper than biochar.