gluPerspective was removed in OpenGL 3.1, any replacements?

Use GLM.

glm::mat4 projection = glm::perspective(
  // FOV & aspect
  60.0f, 16.0f / 10.0f, 
  // Near and far planes
  0.001f, 1000f);

// If you're using the now deprecated matrix stacks
glMatrixMode(GL_PROJECTION);
glLoadMatrixf(glm::value_ptr(projection));

// if you're using the new shader based pipelines
GLint projectionUniformLocation = ...;
glUniformMatrix4fv(projectionUniformLocation, 1, GL_FALSE, 
  glm::value_ptr(projection));

Note, if you have GLM_FORCE_RADIANS defined then you should use radians in the perspective function, not degrees...

glm::mat4 projection = glm::perspective(
  // FOV & aspect
  PI / 3.0f, 16.0f / 10.0f, 
  // Near and far planes
  0.001f, 1000f);

Copied from one of my older projects:

// The following code is a fancy bit of math that is eqivilant to calling:
// gluPerspective( fieldOfView/2.0f, width/height , 0.1f, 255.0f )
// We do it this way simply to avoid requiring glu.h
GLfloat zNear = 0.1f;
GLfloat zFar = 255.0f;
GLfloat aspect = float(width)/float(height);
GLfloat fH = tan( float(fieldOfView / 360.0f * 3.14159f) ) * zNear;
GLfloat fW = fH * aspect;
glFrustum( -fW, fW, -fH, fH, zNear, zFar );

You have to compute the matrix manually and then pass it to OpenGL.

Computing the matrix

This snippet of code is based on the gluPerspective documentation.

 void BuildPerspProjMat(float *m, float fov, float aspect,
 float znear, float zfar)
 {
  float f = 1/tan(fov * PI_OVER_360);

  m[0]  = f/aspect;
  m[1]  = 0;
  m[2]  = 0;
  m[3]  = 0;

  m[4]  = 0;
  m[5]  = f;
  m[6]  = 0;
  m[7]  = 0;

  m[8]  = 0;
  m[9]  = 0;
  m[10] = (zfar + znear) / (znear - zfar);
  m[11] = -1;

  m[12] = 0;
  m[13] = 0;
  m[14] = 2*zfar*znear / (znear - zfar);
  m[15] = 0;
 }

There is a C++ library called OpenGL Mathematics that may be useful.

Loading the Matrix in OpenGL 3.1

I am still new to the OpenGL 3.1 API, but you need to update a matrix on the GPU and then make use of it in your vertex shader to get the proper perspective. The following code just loads the matrix using glUniformMatrix4fv onto the video card.

{
  glUseProgram(shaderId);
  glUniformMatrix4fv(glGetUniformLocation(shaderId, "u_proj_matrix"),
                     1, GL_FALSE, theProjectionMatrix);
  RenderObject();
  glUseProgram(0);
}

A simple vertex shader from a random blog (found through stack overflow).

attribute vec4      a_position;
attribute vec4      a_color;

varying vec4        v_color;

uniform mat4 u_proj_matrix;
uniform mat4 u_model_matrix;

void main() {
  mat4 mvp_matrix = u_proj_matrix * u_model_matrix;
  v_color = a_color;
  gl_Position = mvp_matrix * a_position;
}