Now that there are already vaccines that are said to have passed trials and are good to go for mass distribution, such as the ones from Pfizer, Moderna, and Astra Zeneca. The issue and challenges that countries have to face are limited supplies, approval by local government, and prioritization.
Different countries have used different strategies to go about distribution. In the United Kingdom, they have made the distribution more centralized wherein all processes and prioritization will come from London.
In the U.S. on the other hand, the Trump administration has made it very decentralized wherein they are leaving all the decision-making to the separate states. It is said that the vaccines in the U.S. are divided into the population and not the specific need of the state due to affected cases.