Short answers, pulled from the story.
The Livonian War began on the 22nd of January 1558 when Ivan IV launched an invasion following a treaty alliance between Livonia and Poland-Lithuania. Internal divisions within the Teutonic Order and weak central authority left the region unable to defend itself against external threats.
Main participants included Russia under Ivan IV, Sweden under Eric XIV and Gustavus Adolphus, Denmark-Norway under Frederick II, and the Polish-Lithuanian Commonwealth led by Stephen Báthory. Local entities such as the Duchy of Courland and various bishoprics also played significant roles throughout the conflict.
Negotiations led by Antonio Possevino resulted in the 1582 Truce of Jam Zapolski which forced Russia to surrender all areas in Livonia it still held plus Dorpat to the Commonwealth. The armistice lasted ten years and was renewed twice in 1591 and 1601 before fighting resumed.
Stephen Báthory reduced privileges granted by Sigismund regarding regained territories while Polish gradually replaced German as the administrative language. Local clergy and Jesuits embraced Counter-Reformation with Roman Catholic Church revenues confiscated from Protestants though the population did not convert en masse.
The Treaty of Stolbovo signed in 1617 required Sweden to cede Ingria and Kexholm along with the bulk of the Duchy of Livonia to Russia. Estonia and Livonia formally capitulated to Russia during the Great Northern War in 1710 and this status was formalized in the Treaty of Nystad.