The "Late Era Big Four" refers to the oil fields producing the most up until peak oil, and for some years afterwards. The peaking of these four fields at roughly the same time created a perfect storm, which reduced world oil "production" substantially over the next few years. All of these fields used advanced technology (horizontal drilling, water pumping, etc) to get out oil at super-fast rates up until their peaking, but this led to their ultra-fast decline rates, too.
Ghawar is the largest conventional oil field ever, and was responsible for roughly 60% of Saudi Arabia's oil exports up until its peak in 1996. It accounted for around 6% of all the oil produced each year in the world. More than 10 years later, it is still producing oil, though at less than 20% of its peak. The Ghawar had various sections, or sub-fields, called Ain Dar, Shedgum, Uthmaniyah, Hawiyah, and Haradh, from north to south. The northern areas were exploited first, and had the largest and highest-quality reserves. As of 2007, Ain Dar and Shedgum have been plugged and only the other three areas are still in production. Terrorist attacks have also taken their toll, and have led to some well infrastructure being destroyed.
Kuwait's largest oil field, this was another major producer. It peaked in 1993 and stayed relatively steady until 1995, at which point it entered its depletion spiral to empty. Currently, it is producing around 30% of its peak production. Terrorists, mostly originating in Iraq, have also been setting wells on fire as of 2004.
Mexico's premier field, this peaked in 1994 and has shown one of the highest depletion rates of all the major fields. Now, it is just producing at around 10% of its peak. It is offshore, so the oil is more expensive to obtain than from the other fields, but on the other hand, it is more protected from terrorists than the other fields. Already by 1997, Mexico stopped exporting its oil, and now uses all of its oil domestically, while trying its best to import more needed oil.
The major Chinese field has not figured as much into the international realm as the other fields, because China had not been exporting much oil, but rather using it for its own consumption for years before peak oil. However, China still has 1/6th of all the people on earth, and Daqing's peaking in 1994 had (and still has) a huge impact on the Chinese people. (More non-Daqing oil found in Bohai Bay in 2003 is being exploited as quickly as possible, perhaps leading to a softer crash, but also effectively making China's reserves nil in the long term, that is China has no backup supply. This is similar to what happened when The United States exploited its Arctic National Wildlife Refuge (ANWR) reserves quickly, ensuring no oil for future generations.)