JavaFX FXML controller - constructor vs initialize method

In a few words: The constructor is called first, then any @FXML annotated fields are populated, then initialize() is called.

This means the constructor does not have access to @FXML fields referring to components defined in the .fxml file, while initialize() does have access to them.

Quoting from the Introduction to FXML:

[...] the controller can define an initialize() method, which will be called once on an implementing controller when the contents of its associated document have been completely loaded [...] This allows the implementing class to perform any necessary post-processing on the content.

In Addition to the above answers, there probably should be noted that there is a legacy way to implement the initialization. There is an interface called Initializable from the fxml library.

import javafx.fxml.Initializable;

class MyController implements Initializable {
    @FXML private TableView<MyModel> tableView;

    @Override
    public void initialize(URL location, ResourceBundle resources) {
        tableView.getItems().addAll(getDataFromSource());
    }
}

Parameters:

location - The location used to resolve relative paths for the root object, or null if the location is not known.
resources - The resources used to localize the root object, or null if the root object was not localized. 

And the note of the docs why the simple way of using @FXML public void initialize() works:

NOTE This interface has been superseded by automatic injection of location and resources properties into the controller. FXMLLoader will now automatically call any suitably annotated no-arg initialize() method defined by the controller. It is recommended that the injection approach be used whenever possible.

The initialize method is called after all @FXML annotated members have been injected. Suppose you have a table view you want to populate with data:

class MyController { 
    @FXML
    TableView<MyModel> tableView; 

    public MyController() {
        tableView.getItems().addAll(getDataFromSource()); // results in NullPointerException, as tableView is null at this point. 
    }

    @FXML
    public void initialize() {
        tableView.getItems().addAll(getDataFromSource()); // Perfectly Ok here, as FXMLLoader already populated all @FXML annotated members. 
    }
}