At first, Robert A. Iger, Disney’s chief executive, seemed poised to easily defeat Trian. (Blackwells was never much of a threat.) Prominent Disney shareholders like George Lucas and Laurene Powell Jobs lined up to back him. Disney family members, including Abigail E. Disney, blasted Trian and Blackwells as “wolves in sheep’s clothing.” Analysts (Guggenheim, Macquarie) and shareholder advisory firms (Glass Lewis, ValueEdge) threw cold water on Mr. Peltz’s campaign.

But it has evolved into a much closer contest.

Mr. Iger’s job is not at stake. Now 73 and in his second stint as chief executive, he has vowed to leave Disney for good at the end of 2026. A loss, however, would taint his legacy — and potentially disrupt the company’s approach to streaming, theme park expansion and even the messages embedded in its movies.

Here is what to know.

Disney is likely to win, but there are no guarantees.

In recent days, Disney has received crucial support in its effort to keep the dissidents off its board. BlackRock, which owns about 80 million Disney shares, voted to elect Disney’s slate on Monday, as did T. Rowe Price, which owns about nine million. Vanguard, which owns about 146 million shares, gave Disney its vote on Tuesday.

But the activists also have supporters. ISS, an influential proxy advisory firm, partly sided with Mr. Peltz, criticizing Disney’s succession planning. Mr. Peltz also won the backing of Egan-Jones, another advisory firm; it faulted Disney for unnecessarily veering into what it called “the killing fields of the culture wars.”

In voting for Mr. Peltz, the California Public Employees’ Retirement System, or CalPERS, which owns about 6.6 million Disney shares, said the company would benefit from “fresh eyes.” It added that Mr. Peltz was “capable of leading needed change in corporate governance.”