Appcompat v21 Toolbar elevation pre-lollipop

This worked for me very well:

<android.support.v7.widget.CardView
    xmlns:card_view="http://schemas.android.com/apk/res-auto"
    android:layout_width="match_parent"
    android:layout_height="wrap_content"
    android:background="@color/primary"
    card_view:cardElevation="4dp"
    card_view:cardCornerRadius="0dp">

    <android.support.v7.widget.Toolbar
        android:id="@+id/toolbar"
        android:layout_width="match_parent"
        android:layout_height="wrap_content"
        android:background="@color/primary"
        android:minHeight="?attr/actionBarSize" />

</android.support.v7.widget.CardView>

Using CardView container for toolbar is a bad idea.

CardView is heavy, especially for low end devices.

The best way is to put a gradient Shadow view below the toolbar. Shadow view must be a direct child to the coordinator layout. ie. The appbar which contains toolbar and shadow View must be siblings.

Add this view component to your layout.

 <View
    android:id="@+id/gradientShadow"
    android:layout_width="match_parent"
    android:layout_height="5dp"
    android:background="@drawable/toolbar_shadow"
    app:layout_behavior="@string/appbar_scrolling_view_behavior"
    app:layout_collapseMode="pin"/>

The drawable toolbar_shadow.xml

<?xml version="1.0" encoding="utf-8"?>
<shape xmlns:android="http://schemas.android.com/apk/res/android"
   android:shape="rectangle">
<gradient
    android:angle="90"
    android:endColor="#33333333"
    android:startColor="@android:color/transparent"/>
</shape>

This will solve the problems in pre-lollipop devices. But we don't want this shadow in lollipop and above devices so make visibility to gone in devices with lollipop and above.

if (Build.VERSION.SDK_INT >= Build.VERSION_CODES.LOLLIPOP) {
        findViewById(R.id.gradientShadow).setVisibility(View.GONE);
}

Done.