I've had to untangle code in massive-sized View Controllers before and it really impeded my ability to navigate content at first. One important thing I realized is that size alone of the View Controller wasn't reason enough to break things apart. There is complexity in having 1 large file and also complexity in having a bunch of little files. Here are some valid reasons to refactor to break a View Controller into smaller parts:
The View Controller shouldn't be doing much more than being the connecting glue between the View and the Model. If you a lot of network connection code, image manipulation code, etc, then consider breaking those out into helper classes.
Multiple Controls with the View Controller as a data source
If you have a bunch of controls on screen that have your View Controller as data source, consider breaking those into separate data source objects and have them be the data source. Or you can also break them into separate View Controllers (like if you View Controller has a table view in addition to other controller, you can break that into its own Table View Controller class).
If you have the exact same code in different View Controllers put that in 1 shared location. That will make your code reusable and help manage the complexity.
Here is some additional advice to minimize View Controller complexity:
Storyboard instead of Programmatic
Creating View elements is a lot of code and frame geometry code is a lot of work as well. If not already consider using auto layout constraints and putting as much of the View elements in the storyboard as possible.
Also be sure to remove unnecessary code/comments. A lot of times a new View Controller file will come with methods you are not using. If you aren't using a method like
didReceiveMemoryWarning then it is safe to take it out. Also, because the View Controller file is so big sometimes it is scary to remove old code or comments. Don't put that off! It only adds to the complexity.
To answer your question about notifications: Notifications aren't a Golden Hammer to use with everything. I find notifications to be useful when multiple View Controllers need to update at the same time because of 1 particular action. Be careful with notifications though, overusing them can cause you a lot of pain trying to track them down.