Repotting houseplants: is it really necessary? How to know when to do it?

Calling to all houseplant experts,

I've had my plants for a couple of years, and they seem happy and growing well. I currently have a flamingo flower and a philodendron (here is a picture of them).

Over the years, I think I have gotten pretty good at taking care of them. One thing that still remains a mystery, though, is repotting and when to do it. I have never done it before, and info online seems confusing and often conflicting.

I live in a small space, so I would prefer not to have to do it, but I can see roots growing out of the bottom of the vases, and the plants are getting rather big: so much so, that my philodendron needs external support to not fall down. Nevertheless, they both keep growing.

So, onto the questions: how does one know when it is necessary to repot a plant to a bigger pot? What happens if I do not do it? And if I must do it, how should it be done? Ideally with minimal resources, since I am very limited on storage space...

And since we're at it: any houseplant-related pro-tips from the veterans?