diff --git a/doc/source/programs/gdalwarp.rst b/doc/source/programs/gdalwarp.rst
index 2f559bdcb716..bccc9778d188 100644
--- a/doc/source/programs/gdalwarp.rst
+++ b/doc/source/programs/gdalwarp.rst
@@ -214,10 +214,10 @@ with control information.
 
 .. option:: -et <err_threshold>
 
-    Error threshold for transformation approximation in source pixel units.
-    Defaults to 0.125 source pixels unless the ``RPC_DEM`` transformer
-    option is specified, in which case, an exact transformer, i.e.
-    ``err_threshold=0``, will be used).
+    Error threshold for transformation approximation, expressed as a number of
+    source pixels. Defaults to 0.125 pixels unless the ``RPC_DEM`` transformer
+    option is specified, in which case an exact transformer, i.e.
+    ``err_threshold=0``, will be used.
 
 .. option:: -refine_gcps <tolerance> [<minimum_gcps>]
 
@@ -490,21 +490,43 @@ with control information.
     The destination file name.
 
 
-Mosaicing into an existing output file is supported if the output file
-already exists. The spatial extent of the existing file will not
-be modified to accommodate new data, so you may have to remove it in that case, or
-use the -overwrite option.
+Overview
+--------
 
-Polygon cutlines may be used as a mask to restrict the area of the
-destination file that may be updated, including blending.  If the OGR
-layer containing the cutline features has no explicit SRS, the cutline
-features must be in the SRS of the destination file. When writing to a
-not yet existing target dataset, its extent will be the one of the
-original raster unless -te or -crop_to_cutline are specified.
+:program:`gdalwarp` transforms images between different coordinate reference
+systems and spatial resolutions.
+
+First, :program:`gdalwarp` must determine the extent and resolution of the
+output, if these have not been specified using :option:`-te` and :option:`-tr`.
+These are determined by transforming a sample of points from the source CRS to
+the destination CRS. Details of the procedure can be found in the documentation
+for :cpp:func:`GDALSuggestedWarpOutput`. If multiple inputs are provided to
+:program:`gdalwarp`, the output extent will be calculated to cover all of them,
+at a resolution consistent with the highest-resolution input.
+
+Once the dimensions of the output image have been determined,
+:program:`gdalwarp` divides the output image into chunks that can be processed
+independently within the amount of memory specified by :option:`-wm`.
+:program:`gdalwarp` then iterates over scanlines in these chunks, and for each
+output pixel determines the set of source pixels that contribute to the value
+of the output pixel. These source pixels are provided to a function that
+performs the resampling algorithm selected with :option:`-r`.
+
+Writing to an existing file
+---------------------------
+
+Mosaicing into an existing output file is supported if the output file already
+exists. The spatial extent of the existing file will not be modified to
+accommodate new data, so you may have to remove it in that case, or use the
+:option:`-overwrite` option.
+
+Polygon cutlines may be used as a mask to restrict the area of the destination
+file that may be updated, including blending.  If the OGR layer containing the
+cutline features has no explicit SRS, the cutline features are assumed to be in
+the SRS of the destination file. When writing to a not yet existing target
+dataset, its extent will be the one of the original raster unless :option:`-te`
+or :option:`-crop_to_cutline` are specified.
 
-Starting with GDAL 3.1, it is possible to use as output format a driver that
-only supports the CreateCopy operation. This may internally imply creation of
-a temporary file.
 
 .. _gdalwarp_nodata:
 
@@ -580,13 +602,13 @@ use :option:`-et 0` which disables this approximator entirely.
 Vertical transformation
 -----------------------
 
-While gdalwarp can essentially perform coordinate transformations in the 2D
-space, it can perform as well vertical transformations. This is automatically
-enabled when the 2 following conditions are met:
+While gdalwarp is most commonly used to perform coordinate transformations in the 2D
+space, it can also perform vertical transformations. Vertical transformations are
+automatically performed when the following two conditions are met:
 
 - at least one of the source or target CRS has an explicit vertical CRS
-  (as part of a compound CRS) or is a 3D (generally geographic) CRS,
-- and the raster has a single band.
+  (as part of a compound CRS) or is a 3D (generally geographic) CRS, and
+- the raster has a single band
 
 This mode can also be forced by using the :option:`-vshift` (this is
 essentially useful when the CRS involved are not explicitly 3D, but a