French under Napoleon III & Italians (more correctly Piedmont-Sardinia) under Victor-Emmanuel II (later first king of Italy) v. Austrians under the young Emperor Franz Joseph (with Germans in reserve). Italians were trying to regain Lombardy and Venetia from five generations of Austrian rule. France had agreed to help and in exchange would receive Savoy and Nice.
Solferino was the greatest land battle since Austerlitz, with 270,000 men clashing for 15 hours from 4 a.m. to 7 p.m. There were 40,000 casualties. In the end the Austrian forces were driven from their positions but the carnage was so great that Napoleon III decided he could not continue with the war; by 11th July he had signed a peace treaty gaining Lombardy for Victor Emmanuel but leaving the Austrians with Venetia. On hearing the news, V-E's prime minister Cavour resigned, declaring that Italy had been betrayed. Italy had to fight another war in 1865 to regain Venetia.
The battle was witnessed by Swiss businessman Henri Dunant (pictured right), who happened to be in the area whilst on a business trip to Italy. He was so deeply moved by the plight of the many wounded, many of whom went on to die of wounds or be finished off by enemy forces, that he wrote his famous book "A Memory of Solferino", and is credited with founding the Red Cross. By 1864, 14 nations had signed the Geneva Convention which covered the treatment of wounded and prisoners.
An grisly extract from his book :
"For several days running I handed out tobacco, pipes and cigars, in the churches and hospitals, where the smell of the tobacco, smoked by hundreds of men, was of great value against the pungent stench which arose as the result of crowding so many patients together in stifling hot buildings. The stocks of tobacco in Brescia were very soon exhausted, and more had to be brought from Milan. Only tobacco could lessen the fears which the wounded men felt before an amputation. Many underwent their operation with a pipe in their mouths, and a number died still smoking"
[thanks to JL for contributing most of this post]