The API is jQuery like;
// find some pages:
$pages->find('template=skyscraper, architect=john, sort=title')->limit(4);

// mutate
$pages->get('title=Hello You')->set('title', 'HelloWorld')->save();
$pages->get('title=Old')->trash(); // trash page

// check user…
$user->isLogedin();
echo $user->name; // guest
$session->login($name, $pass);
$session->logout();

// redirect
$session->redirect($url);

ProcessWire is heavily based on custom fields. All objects (Pages) inside ProcessWire are based on extensible templates comprised of fields that can be easily defined. Many useful fields come prebuilt and they can be extended with modules.

By default, ProcessWire comes with 0 assumption on how you handle the output. You have 100% freedom on how you want to develop the frontend. Want to plain output stuff, go ahead. Want to use any number of Templating Engine, do it. Just use as Headless-CMS, okay!

Either using the modules already available or writing your own module, using the jQuery-like API.

Processwire is extremely easy to learn. Consider this:
echo $pages->get('title=Hello World')->title; // "Hello World"
echo $pages->get('title=Hello World')->parent->title; // "Home"
echo $pages->find('Template=Category')->count; // 126
echo $pages->find('Template=Category')->each('title'); // ['Audio', 'Video' …]

Selectors are so powerful but yet so easy.

Check out the cheatsheet.

The way you fetch, access and manipulate objects (Pages) in ProcessWire is extremely powerful and easy. You can receive any page and its custom fields, filter, travers, add…

You will always find one to respond politely in the forums. Sometimes even the creator Ryan Cramer himself.

Source available on GitHub.