What's the difference between setWebViewClient vs. setWebChromeClient in Android?
From the source code (http://is.gd/c8VSw):
// Instance of WebViewClient that is the client callback.
private volatile WebViewClient mWebViewClient;
// Instance of WebChromeClient for handling all chrome functions.
private volatile WebChromeClient mWebChromeClient;
// SOME OTHER SUTFFF.......
/**
 * Set the WebViewClient.
 * @param client An implementation of WebViewClient.
 */
public void setWebViewClient(WebViewClient client) {
    mWebViewClient = client;
}
/**
 * Set the WebChromeClient.
 * @param client An implementation of WebChromeClient.
 */
public void setWebChromeClient(WebChromeClient client) {
    mWebChromeClient = client;
}
Using WebChromeClient allows you to handle Javascript dialogs, favicons, titles, and the progress. Take a look of this example: Adding alert() support to a WebView
At first glance, there are too many differences WebViewClient & WebChromeClient. But, basically: if you are developing a WebView that won't require too many features but rendering HTML, you can just use a WebViewClient. On the other hand, if you want to (for instance) load the favicon of the page you are rendering, you should use a WebChromeClient object and override the onReceivedIcon(WebView view, Bitmap icon).
Most of the times, if you don't want to worry about those things... you can just do this:
webView= (WebView) findViewById(R.id.webview); 
webView.setWebChromeClient(new WebChromeClient()); 
webView.setWebViewClient(new WebViewClient()); 
webView.getSettings().setJavaScriptEnabled(true); 
webView.loadUrl(url); 
And your WebView will (in theory) have all features implemented (as the android native browser).