I believe project management will become more holistic. It will incorporate more sustainability methods. The project types will be more widespread. With projects we create the future.
People need structure, so we need methodologies etc., but in the end, it is the people who go the last mile, or the extra mile, to make the project succeed. Hence soft skills should be more in the center of project management training and delivery.
Many people consider cultural differences as challenges or risks on project teams. While that may often be true, I see it differently. Cultural diversity on teams can provide opportunities to identify and explore new ideas and possible solutions. Diversity can thus contribute to innovation and agility, in my opinion. I think the best leaders recognize the potential value of diversity, are open to differences and act accordingly.
I think it is a mistake to see waterfall and agile as mutually exclusive. All forms of project management have always included a degree of agility. Agility is simply the best way to respond to uncertainty and even the most thoroughly designed projects have a degree of uncertainty. Approaches like Concurrent Engineering were around decades before Agile and take similar approaches.
One of the first steps a project manager can take is to gain competence in speaking truth to power and influencing without authority.