Webview HTTPS handshake failed

If you do not upload your app to the Play Store, you can just ignore SSL certificate errors:

@Override
public void onReceivedSslError(WebView view, SslErrorHandler handler, SslError error) {
    handler.proceed(); // Ignore SSL certificate errors
}

This problem is because the android versions under 4.4 does not support new versions TLS 1.1, TLS 1.2, which almost all sites use these versions.

Here is a list of android versions and support for TLS.