Why does the U.S. want better relations?
One reason analysts point to is Iran.
The U.S. may seek Venezuela's help in imposing sanctions on Iran for its nuclear program, senior American officials said.
Iran and Venezuela have close relations.
Last year, Iranian President Mahmoud Ahmadinejad traveled to Venezuela as part of a tour of Latin America. The two leaders vowed to work together.
Over the years, the two nations have signed more than 270 accords, including trade deals and agreements on construction projects, car and tractor factories, energy initiatives and banking programs.
The other is oil.
Will the death affect Venezuela's oil supply?
It may, some analysts say -- and that would be a huge concern for the United States.
Venezuela remains the fourth-biggest oil supplier to the U.S. market. If the power vacuum causes exports to drop, U.S. consumers could face higher prices and another hit to the U.S. economy, analysts say.
When is Chavez's funeral planned?
Venezuela is planning a state funeral Friday that is expected to be attended by regional and world leaders and dignitaries, including Ahmadinejad. Chavez will be buried after the ceremony but officials have not said where.
What has been the reaction to the death?
Chavez allies, such as leaders of Ecuador, China, Iran and Cuba, expressed sorrow and solidarity.
Bolivian President Evo Morales' voice cracked as he spoke to reporters, describing Chavez as someone "who gave all his life for the liberation of the Venezuelan people ... of all the anti-imperialists and anti-capitalists of the world."
Longtime critics had a different view, with some saying his death could be seen as an opportunity for change.
"At this key juncture, I hope the people of Venezuela can now build for themselves a better, brighter future based on the principles of freedom, democracy," Canada's Prime Minister Stephen Harper said.
Opinions varied too among CNN readers who offered their thoughts on iReport.
"We can't in the U.S. always looks at somebody and just label them as a dictator," said Omekongo Dibinga, a motivational speaker from Washington DC.
"At the end of the day, he's somebody who really wanted to help others to do better. For that he should be respected, even by those who did not agree with his policies."
Carlos Quijada said he fled Venezuela 10 years ago as a teen because there was no future there.
"My life was completely altered because of that man. And I will not hide the fact that I am happy that he is no longer alive," he said. "I left Venezuela because my brother got kidnapped, our house got burglarized, cars stolen, my parents had an import business and the currency control made it impossible for them to import anything anymore."