QT overview/tutorial?

You can try C++ GUI Programming with QT4

I recommend reading the following conceptual documents from the Qt Documentation itself:

Object Model presents the why and how Qt extends the plain C++ object model with the metaobject compiler and what features it adds.
Object Trees and Ownership illustrates the preferred way of managing dynamically allocated QObjects in Qt. (Notice: preferred, not mandatory.)
Signals and Slots explains this basic concept in greater depth.
Container Classes presents the STL-compatible, collection-like classes adopted by the Qt API. An important concept, implicit sharing, is also introduced.
The Qt Resource System describes how data can be embedded in your program or library and accessed at runtime through a special file system.
You're doing it wrong is a blog post explaining how to properly use the QThread class. This is a good read because the documentation and all examples are wrong.
Debugging Techniques are a few debugging tips that are peculiar to Qt. In particular, it explains how to use the qDebug construct.

Here's the full list of core documents.

Widgets and Layouts defines what widgets are and how they are assembled on the screen.
Window and Dialog Widgets explains the subtle difference between what Qt treats as windows and what it treats as widgets.
Layout Management goes into further detail about widget layout. If you use the built in UI designer, you'll rarely need to fiddle with layout classes directly, but the concepts are nevertheless important.
Paint System is how Qt draws stuff.
Coordinate System illustrates how Qt interprets graphics coordinates on painting devices.
Qt Quick is the new way of building pretty UIs.

Here's the full list of GUI and Graphics documents.

By the time you understand the basics, the rest of the API is very cohesive, consistent and easy to grasp.

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