By the "Avatar Crisis" series, do you mean the Shadow of the Avatar trilogy, or just the Avatar trilogy?
The Avatar trilogy (Shadowdale, Tantras, and Waterdeep) is the actual three novel set describing the Time of Troubles and how it came about and ended. Its the defining "shake-up" of the Realms.
The Shadow of the Avatar trilogy (Shadows of Doom, Cloak of Shadows, and All Shadows Fled) is the trilogy describing what the "movers and shakers" of the Realms, such as Elminster, Khelben, the Seven Sisters and the like, were doing during the Time of Troubles.
Other good books for major events in the Realms are Prince of Lies the sequel to the Avatar trilogy ten years after the fact, and its own sequel Crucible: The Trial of Cyric the Mad three years after that.
Shortly after that but not directly related is the Cormyr trilogy (Cormyr: A Novel, Beyond the High Road, and Death of a Dragon). These events detail the largest and most powerful country in Faerun, and the events that rock it to its core.
An even more recent, big shake up in the Realms is detailed in the Return of the Archwizards trilogy (The Summoning, The Siege, and The Sorcerer), wherein an ancient force returns to Faerun, and an even older evil is released.
Of course, there are many more books than these, many of which have a large impact on the Realms, but you can't go wrong with the ones mentioned here. Good luck and good reading!