JEditorPane with Javascript and CSS support

+1 to mKorbel.

Use JavaFX WebView which supports HTML5 by integrating it with Swing.

Here is an example:

import java.awt.*;
import java.awt.event.*;
import java.net.MalformedURLException;
import java.net.URL;
import javafx.application.Platform;
import javafx.beans.value.ChangeListener;
import javafx.beans.value.ObservableValue;
import static javafx.concurrent.Worker.State.FAILED;
import javafx.embed.swing.JFXPanel;
import javafx.event.EventHandler;
import javafx.scene.Scene;
import javafx.scene.web.WebEngine;
import javafx.scene.web.WebEvent;
import javafx.scene.web.WebView;
import javax.swing.*;

public class SimpleSwingBrowser implements Runnable {
    private JFXPanel jfxPanel;
    private WebEngine engine;

    private JFrame frame = new JFrame();
    private JPanel panel = new JPanel(new BorderLayout());
    private JLabel lblStatus = new JLabel();

    private JButton btnGo = new JButton("Go");
    private JTextField txtURL = new JTextField();
    private JProgressBar progressBar = new JProgressBar();

    private void initComponents() {
        jfxPanel = new JFXPanel();

        createScene();

        ActionListener al = new ActionListener() {
            @Override public void actionPerformed(ActionEvent e) {
                loadURL(txtURL.getText());
            }
        };

        btnGo.addActionListener(al);
        txtURL.addActionListener(al);

        progressBar.setPreferredSize(new Dimension(150, 18));
        progressBar.setStringPainted(true);

        JPanel topBar = new JPanel(new BorderLayout(5, 0));
        topBar.setBorder(BorderFactory.createEmptyBorder(3, 5, 3, 5));
        topBar.add(txtURL, BorderLayout.CENTER);
        topBar.add(btnGo, BorderLayout.EAST);


        JPanel statusBar = new JPanel(new BorderLayout(5, 0));
        statusBar.setBorder(BorderFactory.createEmptyBorder(3, 5, 3, 5));
        statusBar.add(lblStatus, BorderLayout.CENTER);
        statusBar.add(progressBar, BorderLayout.EAST);

        panel.add(topBar, BorderLayout.NORTH);
        panel.add(jfxPanel, BorderLayout.CENTER);
        panel.add(statusBar, BorderLayout.SOUTH);

        frame.getContentPane().add(panel);
    }

    private void createScene() {

        Platform.runLater(new Runnable() {
            @Override public void run() {

                WebView view = new WebView();
                engine = view.getEngine();

                engine.titleProperty().addListener(new ChangeListener<String>() {
                    @Override
                    public void changed(ObservableValue<? extends String> observable, String oldValue, final String newValue) {
                        SwingUtilities.invokeLater(new Runnable() {
                            @Override public void run() {
                                frame.setTitle(newValue);
                            }
                        });
                    }
                });

                engine.setOnStatusChanged(new EventHandler<WebEvent<String>>() {
                    @Override public void handle(final WebEvent<String> event) {
                        SwingUtilities.invokeLater(new Runnable() {
                            @Override public void run() {
                                lblStatus.setText(event.getData());
                            }
                        });
                    }
                });

                engine.locationProperty().addListener(new ChangeListener<String>() {
                    @Override
                    public void changed(ObservableValue<? extends String> ov, String oldValue, final String newValue) {
                        SwingUtilities.invokeLater(new Runnable() {
                            @Override public void run() {
                                txtURL.setText(newValue);
                            }
                        });
                    }
                });

                engine.getLoadWorker().workDoneProperty().addListener(new ChangeListener<Number>() {
                    @Override
                    public void changed(ObservableValue<? extends Number> observableValue, Number oldValue, final Number newValue) {
                        SwingUtilities.invokeLater(new Runnable() {
                            @Override public void run() {
                                progressBar.setValue(newValue.intValue());
                            }
                        });
                    }
                });

                engine.getLoadWorker()
                        .exceptionProperty()
                        .addListener(new ChangeListener<Throwable>() {

                            public void changed(ObservableValue<? extends Throwable> o, Throwable old, final Throwable value) {
                                if (engine.getLoadWorker().getState() == FAILED) {
                                    SwingUtilities.invokeLater(new Runnable() {
                                        @Override public void run() {
                                            JOptionPane.showMessageDialog(
                                                    panel,
                                                    (value != null) ?
                                                    engine.getLocation() + "\n" + value.getMessage() :
                                                    engine.getLocation() + "\nUnexpected error.",
                                                    "Loading error...",
                                                    JOptionPane.ERROR_MESSAGE);
                                        }
                                    });
                                }
                            }
                        });

                jfxPanel.setScene(new Scene(view));
            }
        });
    }

    public void loadURL(final String url) {
        Platform.runLater(new Runnable() {
            @Override public void run() {
                String tmp = toURL(url);

                if (tmp == null) {
                    tmp = toURL("http://" + url);
                }

                engine.load(tmp);
            }
        });
    }

    private static String toURL(String str) {
        try {
            return new URL(str).toExternalForm();
        } catch (MalformedURLException exception) {
                return null;
        }
    }

    @Override public void run() {

        frame.setPreferredSize(new Dimension(1024, 600));
        frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);

        initComponents();

        loadURL("http://oracle.com");

        frame.pack();
        frame.setVisible(true);
    }

    public static void main(String[] args) {
        SwingUtilities.invokeLater(new SimpleSwingBrowser());
    }
}

This link also provides some helpful examples of WebView including demonstrating use of JavaScript

References:

• Integrating JavaFX into Swing Applications
• Add Java FX 2.0 to existing Netbeans project

• current Java6/7 supporting only (upto) Html 3.2 with reduced support for css,

• for Html5 and quite full css support to use JavaFx Components,

• there are custom Java libraries with (full???) support of Html4/5, css and js but I'd be suggest to use JavaFX instead