I use new android.support.v4.widget.NestedScrollView and I faced with issue.
Here is my layout:
<android.support.design.widget.AppBarLayout
    android:layout_width="match_parent"
    android:layout_height="250dp">
    <android.support.design.widget.CollapsingToolbarLayout
        android:layout_width="match_parent"
        android:layout_height="match_parent"
        app:contentScrim="?attr/colorPrimary"
        app:layout_scrollFlags="scroll|exitUntilCollapsed">
        <RelativeLayout
            android:layout_width="match_parent"
            android:layout_height="wrap_content"
            app:layout_collapseMode="parallax"
            app:layout_collapseParallaxMultiplier="0.7">
             <!-- some views inside -->
        </RelativeLayout>
        <android.support.v7.widget.Toolbar
            android:layout_width="match_parent"
            android:layout_height="?attr/actionBarSize"
            app:popupTheme="@style/ThemeOverlay.AppCompat.Light"
            app:layout_collapseMode="pin"
            />
    </android.support.design.widget.CollapsingToolbarLayout>
    </android.support.design.widget.AppBarLayout>
    <android.support.v4.widget.NestedScrollView
    android:layout_width="match_parent"
    android:layout_height="match_parent"
    app:layout_behavior="@string/appbar_scrolling_view_behavior"
    >
    <WebView
        android:id="@+id/content"
        android:layout_width="match_parent"
        android:layout_height="wrap_content"/>
</android.support.v4.widget.NestedScrollView>
I need to load html inside textView, so I make:
content.setText(Html.fromHtml(htmlString));
And it looks strange. My textview placed at the bottom of screen.

After I swipe on the text it starts to look normal.

And I think textview is not only view with these issue.
I tried use webview, but it even does not show content (I think due to incorrect height computation).
So I need webview or textview to correct work with NestedScrollView.
P.S. If I set textview height in dp then text looks correctly, but I need wrap_content for height. 
Finally I need to use WebView. Alex Facciorusso answer partly works, but I faced with another issue. When WebView content has some specific height then I can see part of the content, but I can't scroll down. 
Example:

Read a lot of posts, and custom implementation of WebView as well, but I was keen about experimenting with attributes and found out what works for me, which is this:
For NestedScrollView use attribute
android:fillViewport="true"
and for the underlying WebView make sure you are using height as wrap
<WebView
    android:id="@+id/webview"
    android:layout_width="match_parent"
    android:layout_height="wrap_content">
</WebView>
so as a pseudo code you have
<NestedScrollView> // height=  match_parent
 <Parent_layout>//could be Realtive/Linear with height= match_parent
   <Some_View></Some_View>
   <Some_View></Some_View>
   <WebView></WebView> // height=  wrap_content
 </Parent_layout>
</NestedScrollView>
                        A simple workaround will be to add an empty View with 500dp height below your TextView inside of your LinearLayout. That View shall push up your TextView to the right position.
<android.support.v4.widget.NestedScrollView
    app:layout_behavior="@string/appbar_scrolling_view_behavior"
    android:layout_width="match_parent"
    android:layout_height="match_parent">
<!-- Your scrolling content -->
<LinearLayout
    android:layout_width="match_parent"
    android:layout_height="match_parent"
    android:orientation="vertical">
    <TextView
        android:layout_width="match_parent"
        android:layout_height="match_parent"
        android:text="@string/random_text" />
    <View
        android:layout_width="match_parent"
        android:layout_height="500dp"/>
</LinearLayout>
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