Julian Zelizer is a professor of history and public affairs at Princeton University. He is the author of "Jimmy Carter" and "Governing America."

(CNN) -- On Thursday, President Obama and former presidents Jimmy Carter, George H.W. Bush and Bill Clinton are due to attend the grand opening of President George W. Bush's presidential library and archive in Dallas, Texas.

The opening of the library offers an opportunity to think again about the legacy of the Bush presidency. As Obama and the former presidents look around the museum, they will see many exhibits that symbolize how the jury is still out on most of the major issues. Events in the coming years will play a huge role in how history is likely to remember Bush's White House.

There are four big questions about his presidency.

1. How effective and how just were Bush's counterterrorism policies?

Bush came into office much more concerned about domestic issues like education and taxation, but after the 9/11 terror attacks, he invested a great deal of his power in the counterterrorism program.

He and his supporters have felt that the absence of major attacks until last week and that the re-establishment of calm in the United States was a defining achievement. It is not surprising that one of the artifacts that Obama will see during his visit is the bullhorn Bush used in his famous address to first responders who were working at Ground Zero....