Basic idea - navigating between pages is slow, because:

browser waits for network response
it is expensive to redraw the whole page from scratch. Much faster would be to replace innerHTML of the document. At least this is common belief, but there are nuances to that.

History

First solution appeared in 2010. See defunkt/jquery-pjax

Around 2015 "olympic torch" was taken over by turbolinks. Which was part of Rails stack and later replaced by Turbo Drive.

Around the same time there were also:

In 2018 Google jump in on that boat with quicklink

Note: later doesn't mean better, because development didn't stop at the release date. For example, swup recently released v4.

Is it still alive?

Yes.

One would think that with SPA trend (started around 2015) nobody would care about this kind of solutions, but static website still popular. For example Hugo, Astro and others

The devil is in the details

I put all those libraries in one category but they are actually different and use different assumptions. For example,

PJAX uses History API and AJAX (or fetch). It takes over browser navigation mechanism
quicklink on the other side bothers itself only with prefetching/prerendering

Browser history

So we have two main approaches:

don't take over browser navigation
- pros:
- easy to integrate
- cons:
- animations are not possible
- state of the page reseted, like selected tabs, collapsed menu, scroll position in sidebar
- examples: quicklink, @astrojs/prefetch, astro-hover-prefetch, swup preload
take over browser navigation
- pros:
- hard to integrate
- cons:
- animations are possible
- state of the page can be preserved but needs additional work
- examples: pjax, barba, swup, astro-spa

Adaptability

Besides browser navigation we need to take into account:

we don't want to prefetch all the links
- quicklink uses Intersection Observer to detect links within the viewport
- Other approach is to do this on hover, focus, tap
- Some libraries allows to specify which links to prefetch
- Or we can statistically guess
we don't want it to do while browser is busy doing something else. You don't want to degrade user experience
- quicklink uses requestIdleCallback
Making additional requests on mobile devices may cost user additional money
- quicklink uses navigator.connection.effectiveType to detect slow networks, and navigator.connection.saveData to detect data-saver mode

Related functionality

Main subject is to speed up navigation between pages, but there are related functionalities:

animate page navigations, like in swup and barba
replace only part of the page, for example to filter list or table, like in Turbo Frames, swup fragment, astro view transitions
show page preview on hover, like in Obsidian. See also previewbox and astro-link-preview
highlight section if navigated with anchor, like in StakOverflow

I mainly concern myself with static web sites, but in the context of dynamic websites there is so called "HTML over wire" approach:

Complexity with browser history

Basic implementation can look like this

Add global click event listener
on click you fetch remote content
extract element that needs to be replaced (for example main)
replace content with target.innerHTML = response
Push new item to history with history.pushState(state, "", url);

But you need to take care of:

removing event handlers from old HTML
attaching event handlers to new HTML
replacing title, maybe announce it to screen reader
replacing styles
replacing scripts
maybe provide a hook so that it would be possible to integrate analytics
scrolling to top of the page
listen to history for back navigations
maybe resolve relative links
it doesn't preserve state of scroll or tabs

It is an error-prone approach.

To be continued...

While I was doing the research on the subject I stumbled upon:

I will need more time to finish the research

Speed up navigation between pages