How can I use GLSL shaders within Mathematica?

As it turns out, it is entirely possible in 14.0 to write your own custom shaders as this video by Yuzhu Lu demonstrates.

In addition, a number of custom shaders are available to read in:

Mathematica\14.0\SystemFiles\FrontEnd\TextResources\CustomizedShaders.tr

Here is an example where I use a fragment shader to warp an image inside a manipulate:

customShader.frag

#version 330
uniform sampler2D theTexture;
uniform float time;
in vec2 v_texcoord;
out vec4 glFragColor;

void main()
{
    vec2 newcoord = vec2(
        v_texcoord.x + 0.05f*cos(time + 10 * v_texcoord.y),
        v_texcoord.y + 0.05f*sin(time + 10 * v_texcoord.x)
    );

    vec4 texColor = texture(theTexture, newcoord);
    glFragColor = texColor;
}

customShader.vert

#version 330
uniform mat4 mvp_matrix;
in vec4 a_position;
in vec2 a_texcoord;
out vec2 v_texcoord;

void main()
{
    gl_Position = mvp_matrix * a_position;
    v_texcoord = a_texcoord;
}

Remove["Global`*"];
fragmentShader = Import["customShader.frag", "Text"];
vertexShader = Import["customShader.vert", "Text"];
customGLSLShader = <|
   "Name" -> "CustomShader",
   "Attributes" -> <|"a_position" -> "ATTRIB_VERTEX",
     "a_texcoord" -> "ATTRIB_TEXTURECOORD"|>, "Parameters" ->
    <|"Matrix" -> {"mvp_matrix", "TRANSFORMMATRIX", "MATRIX4"}, 
     "Time" -> {"time", 0.0, "NUMBER"}|>,
   "ShaderPrograms" -> <|"GLFragmentProgram" -> fragmentShader,
     "GLVertexProgram" -> vertexShader|>
   |>;
FE`Evaluate[
  Evaluate[
   FEPrivate`AddSurfaceAppearanceDefinition[customGLSLShader]]];
(* Check that it was loaded *)
FE`Evaluate[FEPrivate`ListSurfaceAppearanceDefinitions["CustomShader"]]

tex = ExampleData[{"TestImage", "Mandrill"}];
Manipulate[
 Graphics[{Texture[tex], 
   SurfaceAppearance["CustomShader", "Time" -> t], 
   Rectangle[{0, 0}, {1, 1}]}]
 , {t, 0, 20}]