The incident beginning the Second Opium War is shrouded in contested facts and mystery.  It was alleged that in 1856, Chinese officials boarded a ship called the Arrow. The officials arrested and removed several Chinese that were alleged to be involved in the opium trade. The French claimed at that same time that they were offended by the murder of a French missionary in 1856. 

As a result, the English and the French began joint military operations.  In 1858, the allied forces reached Peking and forced the Chinese into negotiations. The parties met at Tianjin and worked out the treaty bearing the city's name.  Eleven more seaports would be opened.  Permanent foreign embassies were allowed in Peking. China agreed to pay a large indemnity.  Opium and the coolie trade were legalized. 

The next summer the Allies returned to ratify the treaty. The Emperor, however, prevented them from going to Peking. So in 1860, a much larger allied force pressed their way into Peking.  Again the Manchus were at the negotiating table.  The Convention of Peking Agreement resulted and it was agreed the 1858 treaty would be obeyed.