TextView
The TextView widget can be used to display and edit large amounts of formatted text. Like the TreeView, it has a model/view design. In this case the TextBuffer is the model.

The Buffer
Gtk::TextBuffer is a model containing the data for the Gtk::TextView, like the Gtk::TreeModel used by Gtk::TreeView. This allows two or more Gtk::TextViews to share the same TextBuffer, and allows those TextBuffers to be displayed slightly differently. Or you could maintain several Gtk::TextBuffers and choose to display each one at different times in the same Gtk::TextView widget.
The TextView creates its own default TextBuffer, which you can access via the get_buffer() method.
Reference

Iterators

Tags and Formatting

Tags
To specify that some text in the buffer should have specific formatting, you must define a tag to hold that formatting information, and then apply that tag to the region of text. For instance, to define the tag and its properties:

Glib::RefPtr<Gtk::TextBuffer::Tag> refTagMatch =
    Gtk::TextBuffer::Tag::create();
refTagMatch->property_background() = "orange";

You can specify a name for the Tag when using the create() method, but it is not necessary.
The Tag class has many other properties.
Reference

TagTable
Each Gtk::TextBuffer uses a Gtk::TextBuffer::TagTable, which contains the Tags for that buffer. 2 or more TextBuffers may share the same TagTable. When you create Tags you should add them to the TagTable. For instance:

Glib::RefPtr<Gtk::TextBuffer::TagTable> refTagTable =
    Gtk::TextBuffer::TagTable::create();
refTagTable->add(refTagMatch);
//Hopefully a future version of gtkmm will have a set_tag_table() method,
//for use after creation of the buffer.
Glib::RefPtr<Gtk::TextBuffer> refBuffer =
    Gtk::TextBuffer::create(refTagTable);

You can also use get_tag_table() to get, and maybe modify, the TextBuffer's default TagTable instead of creating one explicitly.
Reference

Applying Tags
If you have created a Tag and added it to the TagTable, you may apply that tag to part of the TextBuffer so that some of the text is displayed with that formatting. You define the start and end of the range of text by specifying Gtk::TextBuffer::iterators. For instance:

refBuffer->apply_tag(refTagMatch, iterRangeStart, iterRangeStop);

Or you could specify the tag when first inserting the text:

refBuffer->insert_with_tag(iter, "Some text", refTagMatch);

You can apply more than one Tag to the same text, by using apply_tag() more than once, or by using insert_with_tags(). The Tags might specify different values for the same properties, but you can resolve these conflicts by using Tag::set_priority().

Marks
TextBuffer iterators are generally invalidated when the text changes, but you can use a Gtk::TextBuffer::Mark to remember a position in these situations. For instance,

Glib::RefPtr<Gtk::TextBuffer::Mark> refMark =
    refBuffer->create_mark(iter);

You can then use the get_iter() method later to create an iterator for the Mark's new position.
There are two built-in Marks - insert and selection_bound, which you can access with TextBuffer's get_insert() and get_selection_bound() methods.
Reference

The View
As mentioned above, each TextView has a TextBuffer, and one or more TextViews can share the same TextBuffer.
Like the TreeView, you should probably put your TextView inside a ScrolledWindow to allow the user to see and move around the whole text area with scrollbars.
Reference

Default formatting
TextView has various methods which allow you to change the presentation of the buffer for this particular view. Some of these may be overridden by the Gtk::TextTags in the buffer, if they specify the same things. For instance, set_left_margin(), set_right_margin(), set_indent(), etc.

Scrolling
Gtk::TextView has various scroll_to_*() methods. These allow you to ensure that a particular part of the text buffer is visible. For instance, your application's Find feature might use Gtk::TextView::scroll_to_iter() to show the found text.

Widgets and ChildAnchors
You can embed widgets, such as Gtk::Buttons, in the text. Each such child widget needs a ChildAnchor. ChildAnchors are associated with iterators. For instance, to create a child anchor at a particular position, use Gtk::TextBuffer::create_child_anchor():

Glib::RefPtr<Gtk::TextChildAnchor> refAnchor =
    refBuffer->create_child_anchor(iter);

Then, to add a widget at that position, use Gtk::TextView::add_child_at_anchor():

m_TextView.add_child_at_anchor(m_Button, refAnchor);

Reference

Examples

Simple Example

TextView
Source Code
File: examplewindow.h (For use with gtkmm 3, not gtkmm 2)

#ifndef GTKMM_EXAMPLEWINDOW_H
#define GTKMM_EXAMPLEWINDOW_H

#include <gtkmm.h>

class ExampleWindow : public Gtk::Window
{
public:
  ExampleWindow();
  virtual ~ExampleWindow();

protected:

  void fill_buffers();
  
  //Signal handlers:
  void on_button_quit();
  void on_button_buffer1();
  void on_button_buffer2();

  //Child widgets:
  Gtk::Box m_VBox;

  Gtk::ScrolledWindow m_ScrolledWindow;
  Gtk::TextView m_TextView;
  
  Glib::RefPtr<Gtk::TextBuffer> m_refTextBuffer1, m_refTextBuffer2;

  Gtk::ButtonBox m_ButtonBox;
  Gtk::Button m_Button_Quit, m_Button_Buffer1, m_Button_Buffer2;
};

#endif //GTKMM_EXAMPLEWINDOW_H

File: examplewindow.cc (For use with gtkmm 3, not gtkmm 2)

#include "examplewindow.h"

ExampleWindow::ExampleWindow()
: m_VBox(Gtk::ORIENTATION_VERTICAL),
  m_Button_Quit("_Quit", true),
  m_Button_Buffer1("Use buffer 1"),
  m_Button_Buffer2("Use buffer 2")
{
  set_title("Gtk::TextView example");
  set_border_width(5);
  set_default_size(400, 200);

  add(m_VBox);

  //Add the TreeView, inside a ScrolledWindow, with the button underneath:
  m_ScrolledWindow.add(m_TextView);

  //Only show the scrollbars when they are necessary:
  m_ScrolledWindow.set_policy(Gtk::POLICY_AUTOMATIC, Gtk::POLICY_AUTOMATIC);

  m_VBox.pack_start(m_ScrolledWindow);

  //Add buttons:
  m_VBox.pack_start(m_ButtonBox, Gtk::PACK_SHRINK);

  m_ButtonBox.pack_start(m_Button_Buffer1, Gtk::PACK_SHRINK);
  m_ButtonBox.pack_start(m_Button_Buffer2, Gtk::PACK_SHRINK);
  m_ButtonBox.pack_start(m_Button_Quit, Gtk::PACK_SHRINK);
  m_ButtonBox.set_border_width(5);
  m_ButtonBox.set_spacing(5);
  m_ButtonBox.set_layout(Gtk::BUTTONBOX_END);

  //Connect signals:
  m_Button_Quit.signal_clicked().connect(sigc::mem_fun(*this,
              &ExampleWindow::on_button_quit) );
  m_Button_Buffer1.signal_clicked().connect(sigc::mem_fun(*this,
              &ExampleWindow::on_button_buffer1) );
  m_Button_Buffer2.signal_clicked().connect(sigc::mem_fun(*this,
              &ExampleWindow::on_button_buffer2) );

  fill_buffers();
  on_button_buffer1();

  show_all_children();
}

void ExampleWindow::fill_buffers()
{
  m_refTextBuffer1 = Gtk::TextBuffer::create();
  m_refTextBuffer1->set_text("This is the text from TextBuffer #1.");

  m_refTextBuffer2 = Gtk::TextBuffer::create();
  m_refTextBuffer2->set_text(
          "This is some alternative text, from TextBuffer #2.");

}

ExampleWindow::~ExampleWindow()
{
}

void ExampleWindow::on_button_quit()
{
  hide();
}

void ExampleWindow::on_button_buffer1()
{
  m_TextView.set_buffer(m_refTextBuffer1);
}

void ExampleWindow::on_button_buffer2()
{
  m_TextView.set_buffer(m_refTextBuffer2);
}

File: main.cc (For use with gtkmm 3, not gtkmm 2)

#include "examplewindow.h"
#include <gtkmm/application.h>

int main(int argc, char *argv[])
{
  Glib::RefPtr<Gtk::Application> app = Gtk::Application::create(argc, argv, "org.gtkmm.example");

  ExampleWindow window;

  //Shows the window and returns when it is closed.
  return app->run(window);
}