Here are some of the issues:
The pact created a safe shipping channel for exports from three ports in Ukraine and the early focus has been paving the way for ships that had been trapped in the war-torn country since Russia's invasion in February to leave.
So far, about 370,000 tonnes of agricultural products have been shipped, predominately corn, but also small volumes of soybeans, sunflower oil and sunflower meal. There have not yet been any shipments of wheat.
This partly reflects the timing of Russia's invasion as much of last year's wheat crop had already been exported in February, as it is harvested several months before corn and so tends to be shipped earlier.
There is an estimated three million tonnes of grain in ports that need to be moved first, which will probably take until around mid-September to clear.
Much larger volumes will need to be shipped to have a substantial impact on global supplies.
Ukraine has around 20 million tonnes of grain left over from last year's crop piled up across the country, as well as this year's wheat harvest, which is estimated at about a further 20 million tonnes.
The three ports involved in the deal - Odesa, Chornomorsk and Pivdennyi - have the combined capacity to ship around three million tonnes a month and some expect this level of exports could potentially be achieved in October.
It will, however, need a huge number of ships to transport such a large volume of grain and some shipowners may be wary to enter a war zone, particularly with the threat posed by mines and the high cost of insurance.
Russia and Ukraine accuse each other of planting the many naval mines that now float around the Black Sea. These pose a significant threat and were cited by one crew member on the first ship, the Sierra Leone-flagged Razoni, on Monday, 8 August, as the one thing he feared.
The mines have drifted far from Ukraine's shores, with Romanian, Bulgarian and Turkish military diving teams defusing those that have ended up in their waters.
It could take months to clear them and there was not enough time to do so before the grains pact came into effect.
The Istanbul-based Joint Coordination Centre, which oversees the deal and is made up of Turkish, Russian, Ukrainian and U.N. officials, on Monday published long-awaited procedures on the shipping channel, which aims to alleviate concerns that insurers and shipowners have.
Insurers had previously said they were willing to provide cover if there were arrangements for international navy escorts and a clear strategy to deal with sea mines.
In one of the first steps following the July 22 agreement, Lloyd's of London insurer Ascot and broker Marsh set up a marine cargo and war insurance for grain and food products moving out of Ukrainian Black Sea ports with $50m cover for every voyage.
The cost of overall insurance for ships - which includes separate segments of cover - sailing into Ukrainian ports, however, is likely to remain steep.
Finding enough seafarers willing to sail ships stuck inside Ukraine's ports and also crew vessels calling at Ukrainian ports is set to pose another challenge.
At the start of the conflict there were around 2,000 seafarers from all over the world stranded in Ukrainian ports and that number is now below 450.
U.N. Secretary-General Antonio Guterres said the deal would bring relief to developing countries "on the edge of bankruptcy and the most vulnerable people on the edge of famine".
Ukraine can move up to two million tonnes of grain a month by truck and rail, around half the four million tonnes it shipped through its seaports before the conflict.
The sharp decline in shipments from Ukraine played a role in driving up global food prices at a time when world hunger is on the rise. The Covid-19 pandemic and climate shocks have also contributed to food price inflation.
Russia's invasion of Ukraine has spurred food price inflation by driving up prices of both grains and energy. Russia has slowed its natural gas exports to Europe, blaming Western sanctions on pipeline equipment. Western leaders have accused Moscow of blackmail. More expensive fuel drives up the cost of farming, transporting, processing and packaging food.
If the grain export plan succeeds, a decline in global prices of grains and oilseeds is widely anticipated. Supplies are still tight, though, and Ukraine's harvest this year will be lower than last because the conflict has disrupted farming.
The World Food Programme has warned food prices will remain elevated even if the deal holds.
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