[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

>>1
Improvements:
OMG ENTERPRISE
Insert and add should return a ``correct or incorrect operation'' exit value, as new does.
Add an interface for getting elements by number of element. If you don't do this you are going to BREAK ENCAPSULATION and this is considered bad practice and forces the programmer, i.e. you to do things like

iter = phone_nums->front;
    while (iter) {
        printf("%s\n", (char*)iter->data);
        if (!strcmp("567-8901", (char*)iter->data)) { temp = iter; }
        iter = iter->next;
    }

The list is fine, It should work correctly.