Material Design not styling alert dialogs

when initializing dialog builder, pass second parameter as the theme. It will automatically show material design with API level 21.

AlertDialog.Builder builder = new AlertDialog.Builder(this, AlertDialog.THEME_DEVICE_DEFAULT_DARK);

or,

AlertDialog.Builder builder = new AlertDialog.Builder(this, AlertDialog.THEME_DEVICE_DEFAULT_LIGHT);

UPDATED ON Aug 2019 WITH The Material components for android library:

With the new Material components for Android library you can use the new com.google.android.material.dialog.MaterialAlertDialogBuilder class, which extends from the existing androidx.appcompat.AlertDialog.Builder class and provides support for the latest Material Design specifications.

Just use something like this:

new MaterialAlertDialogBuilder(context)
            .setTitle("Dialog")
            .setMessage("Lorem ipsum dolor ....")
            .setPositiveButton("Ok", /* listener = */ null)
            .setNegativeButton("Cancel", /* listener = */ null)
            .show();

You can customize the colors extending the ThemeOverlay.MaterialComponents.MaterialAlertDialog style:

  <style name="CustomMaterialDialog" parent="@style/ThemeOverlay.MaterialComponents.MaterialAlertDialog">
     <!-- Background Color-->
     <item name="android:background">#006db3</item>
     <!-- Text Color for title and message -->
     <item name="colorOnSurface">@color/secondaryColor</item>
     <!-- Text Color for buttons -->
     <item name="colorPrimary">@color/white</item> 
     ....
  </style>  

To apply your custom style just use the constructor:

new MaterialAlertDialogBuilder(context, R.style.CustomMaterialDialog)

To customize the buttons, the title and the body text check this post for more details.

You can also change globally the style in your app theme:

 <!-- Base application theme. -->
 <style name="AppTheme" parent="Theme.MaterialComponents.Light">
    ...
    <item name="materialAlertDialogTheme">@style/CustomMaterialDialog</item>
 </style>

---

WITH SUPPORT LIBRARY and APPCOMPAT THEME:

With the new AppCompat v22.1 you can use the new android.support.v7.app.AlertDialog.

Just use a code like this:

import android.support.v7.app.AlertDialog

AlertDialog.Builder builder =
       new AlertDialog.Builder(this, R.style.AppCompatAlertDialogStyle);
builder.setTitle("Dialog");
builder.setMessage("Lorem ipsum dolor ....");
builder.setPositiveButton("OK", null);
builder.setNegativeButton("Cancel", null);
builder.show();

And use a style like this:

<style name="AppCompatAlertDialogStyle" parent="Theme.AppCompat.Light.Dialog.Alert">
        <item name="colorAccent">#FFCC00</item>
        <item name="android:textColorPrimary">#FFFFFF</item>
        <item name="android:background">#5fa3d0</item>
    </style>

Otherwise you can define in your current theme:

<style name="AppTheme" parent="Theme.AppCompat.Light">
    <!-- your style -->
    <item name="alertDialogTheme">@style/AppCompatAlertDialogStyle</item>
</style>

and then in your code:

 import android.support.v7.app.AlertDialog

    AlertDialog.Builder builder =
           new AlertDialog.Builder(this);

Here the AlertDialog on Kitkat: