[CodeCritique] Criticize my Linked List

I have implemented linked lists in C as a learning exercise.  I'm a noob ass so tell me how my implementation sucks and I will fix it.  I didn't have a particular use-case in mind when I wrote it.

Header:
// llist.h
#ifndef LLIST_H_
#define LLIST_H_

struct LList;
typedef struct LList LList;

struct LLNode;
typedef struct LLNode LLNode;

struct LList {
    LLNode *front, *back;
};

struct LLNode {
    void *data;
    LLNode *next;
};

LList* llist_new(LList **self);
void llist_add(LList *self, void *v);
void llist_remove(LList *self, LLNode *node);
void llist_insert(LLNode *node, void *v);
void llist_destroy(LList *self);

#endif

C file:
// llist.c
#include <assert.h>
#include <stdlib.h>

#include "llist.h"

// Initialize a new, empty LList, in dynamically allocated memory.
LList *llist_new(LList **self) {
    *self = malloc(sizeof (LList));
    if (self == NULL) { return NULL; }

    (*self)->front = NULL;
    (*self)->back = NULL;

    return *self;
}


// Append a value to the LList.  Creates a new node.
void llist_add(LList *self, void *v) {
    LLNode *node = malloc(sizeof (LLNode));
    assert(node != NULL);

    node->data = v;
    node->next = NULL;

    // Put this node at the back of the list.
    if (self->front != NULL) {
        self->back->next = node;
        self->back = node;
    } else {
        self->back = node;
        self->front = node;
    }
}


// Iterate over the LList to locate a node, and then remove it from the list.
void llist_remove(LList *self, LLNode *node) {
    LLNode *iter_node = self->front;
    LLNode *prev_node = NULL;

    while (iter_node != NULL) {
        if (iter_node == node) {
            if (prev_node != NULL) { prev_node->next = iter_node->next; }
            else { self->front = NULL; }
            free(iter_node);
            return;
        }
        prev_node = iter_node;
        iter_node = iter_node->next;
    }

}


// Insert a value after a particular node.
void llist_insert(LLNode *node, void *v) {
    LLNode *next = node->next;
    LLNode *new_node = malloc(sizeof (LLNode));
   
    new_node->data = v;
    new_node->next = next;
   
    node->next = new_node;
}


void llist_destroy(LList *self) {
    LLNode *iter_node = self->front;

    while (iter_node != NULL) {
        LLNode *next = iter_node->next;
        free(iter_node);
        iter_node = next;
    }

    free(self);
}

Testcase:
// llist_test.c
#include <stdio.h>
#include <stdlib.h>
#include <string.h>

#include "llist.h"

#ifdef _WIN32
char *strdup(char *s);
#endif

int main(void) {
    LList *phone_nums;
    LLNode *iter;

    if (llist_new(&phone_nums) == NULL) { printf("Out of memory."); exit(1); }
    llist_add(phone_nums, strdup("123-4567")); // Yes, I should free() these later...
    llist_add(phone_nums, strdup("890-1234"));
    llist_add(phone_nums, strdup("567-8901"));
    llist_add(phone_nums, strdup("234-5678"));
       
        LLNode *temp = NULL;
    iter = phone_nums->front;
    while (iter) {
        printf("%s\n", (char*)iter->data);
        if (!strcmp("890-1234", (char*)iter->data)) { temp = iter; }
        iter = iter->next;
    }
    puts("");
   
    llist_insert(temp, strdup("BEEP BOOP"));
   
    iter = phone_nums->front;
    while (iter) {
        printf("%s\n", (char*)iter->data);
        if (!strcmp("567-8901", (char*)iter->data)) { temp = iter; }
        iter = iter->next;
    }
    puts("");
   
    llist_remove(phone_nums, temp);
   
    iter = phone_nums->front;
    while (iter) {
        printf("%s\n", (char*)iter->data);
        if (!strcmp("567-8901", (char*)iter->data)) { temp = iter; }
        iter = iter->next;
    }
   
   
    llist_destroy(phone_nums);
    return 0;
}

#ifdef _WIN32
char *strdup(char *s) {
        char *p = malloc(strlen(s) + 1);
        strcpy(p, s);
        return p;
}
#endif

>>84
No matter how you do it, nonstandard C functions are nonstandard C functions.  I would say look at how some of the more popular pieces of open source software handles nonstandard C functions. But I'm afraid that you, along with the other hoshead that is calling me an idiot, wouldn't be able to tell what the programmers do in cases like this.