For 3 years and 7 months, the 7K strong British garrison held out against a combined 40K Franco-Spanish army making the battle for the Rock the largest of the entire series of wars 1778-1783 that Britain fought with pretty much all of its major rivals in what was essentially a world war. 

Unlike previous struggles from 1689 and the first 'Grand Alliance' there was no continental ally to help distract the massive power of France and so on land and at sea Britain fought a desperate struggle to not only keep the empire together, but to stave off invasion. 

Gibraltar was kept alive by technical ingenuity such as the Koehler Depression Carriage (Pictured) which gave the defenders the ability to hit enemies at close range. Innovative leadership by General Eliot also saw a daring sortie of 2.5K successfully wreck the Franco-Spanish trenches and siege guns in late 1781. 

The final attempt to breakthrough was in 1782 when 10 specially constructed floating batteries were constructed to support an amphibious attack. They were specially designed to withstand shore based artillery fire and so the defenders started to heat their cannon balls and in so doing were able to set most of the battery ships on fire. 

Finally, the ability of the Royal Navy to break through the siege and land three relief convoys, the last one in October 1782, allowed the defenders to replenish and convinced the the Franco-Spanish commanders that the siege was futile. 

The Longest Siege in British Military History - Gibraltar 1782