The part of your brain that works stuff into long term memory is normally dormant when you sleep.

When you wake up it turns on slowly, and when you wake up by an interruption (like an alarm clock) it turns on quickly.

Meaning dreams closer to morning are more likely to be remembered.

like Deestan said, this is a memory issue less a feature of the dream issue.

If you want to remember your dreams longer term, write down a few sentences describing them when you wake up. That forces the short term memory information through different processing channels as you write, so it can linger enough to be encoded into long term memory later

IIRC it depends heavily on which phase of sleep you're in when you wake up. If you interrupt actual dream / REM phase you're more likely to remember it.

An aside, how/ why do I remember dreams from years ago?

You have hundreds of dreams a night. You only remember the last one. And since time dilates while dreaming, you really have almost no concept of it at that point, so you come to believe that’s the dream you’ve had all night. But you’ve had countless.

And the reason you don’t remember them all is because they have no impact, like remembering what you had to eat for dinner, 3 weeks ago. Just your brain doing housekeeping.

If you're replaying then in your head, You're building new memories and storing it. Then you're referencing that memory, which in turns build a new memory of that memory.

Look into how memory and recall work, which can help with understanding this process!

Stress plays a big part of it - when you're overburdened you may find yourself not remembering any dreams.

Sadly, there isn't a reliable, well backed up answer to this. There simply hasn't been anything uncovered yet to say for sure how and why dreams are remembered. Hell, there isn't even any definitive evidence for why they exist in the first place. Dreams are very difficult to study, at least with current technology.