Waterfall used to be the go-to delivery method of choice for almost all digital projects. There would be the 4 'D's' as they are sometimes called, Discovery; Definition, Design and Delivery.
Then along came Agile - an alternative approach that allows for greater flexibility. Sprints, retrospectives, scrum masters all allowed for the allocation of resources and time with periodic check-ins as opposed to a fixed scope and delivery schedule. This approach was attractive to clients who wanted to visually see progress on a regular basis rather than a big reveal. What it didn't guarantee however was the completion of the original scope.
To counter, more clients want a hybrid of waterfall and agile, 'watergile'. With the "big reveal" project get delivered in sprints in line with the agile processes while maintaining a minimum feature set within the budget. Some projects also run an upfront waterfall delivery to get to an MVP stage and then move to a set of sprints to see how many additional features can be delivered over a set period. Or vice versa.
It's essential in today's market to ensure that a client's' requirements are fully understood and met. This understanding goes not only with the project scope but how the client's organisation functions and the skill set within their team. It is imperative that no matter what delivery method has been selected that the team tasked with delivery are experienced enough to be able to adapt to their clients' needs and not the other way around.