How to fetch all contacts record in iOS 9 using Contacts Framework

Both other answers do only load contacts from the container with the defaultContainerIdentifier. In a scenario, where the user has more than one container (i.e. an Exchange and an iCloud account which both are used to store contacts), this would only load the contacts from the account that is configured as the default. Therefore, it would not load all contacts as requested by the author of the question.

What you'll probably want to do instead is getting all the containers and iterate over them to extract all contacts from each of them. The following code snippet is an example of how we do it in one of our apps (in Swift):

lazy var contacts: [CNContact] = {
    let contactStore = CNContactStore()
    let keysToFetch = [
        CNContactFormatter.descriptorForRequiredKeysForStyle(.FullName),
        CNContactEmailAddressesKey,
        CNContactPhoneNumbersKey,
        CNContactImageDataAvailableKey,
        CNContactThumbnailImageDataKey]

    // Get all the containers
    var allContainers: [CNContainer] = []
    do {
        allContainers = try contactStore.containersMatchingPredicate(nil)
    } catch {
        print("Error fetching containers")
    }

    var results: [CNContact] = []

    // Iterate all containers and append their contacts to our results array
    for container in allContainers {
        let fetchPredicate = CNContact.predicateForContactsInContainerWithIdentifier(container.identifier)

        do {
            let containerResults = try contactStore.unifiedContactsMatchingPredicate(fetchPredicate, keysToFetch: keysToFetch)
            results.appendContentsOf(containerResults)
        } catch {
            print("Error fetching results for container")
        }
    }

    return results
}()

Objective-C:

//ios 9+
CNContactStore *store = [[CNContactStore alloc] init];
[store requestAccessForEntityType:CNEntityTypeContacts completionHandler:^(BOOL granted, NSError * _Nullable error) {
    if (granted == YES) {
        //keys with fetching properties
        NSArray *keys = @[CNContactFamilyNameKey, CNContactGivenNameKey, CNContactPhoneNumbersKey, CNContactImageDataKey];
        NSString *containerId = store.defaultContainerIdentifier;
        NSPredicate *predicate = [CNContact predicateForContactsInContainerWithIdentifier:containerId];
        NSError *error;
        NSArray *cnContacts = [store unifiedContactsMatchingPredicate:predicate keysToFetch:keys error:&error];
        if (error) {
            NSLog(@"error fetching contacts %@", error);
        } else {
            for (CNContact *contact in cnContacts) {
                // copy data to my custom Contacts class. 
                Contact *newContact = [[Contact alloc] init];
                newContact.firstName = contact.givenName;
                newContact.lastName = contact.familyName;
                UIImage *image = [UIImage imageWithData:contact.imageData];
                newContact.image = image;
                for (CNLabeledValue *label in contact.phoneNumbers) {
                    NSString *phone = [label.value stringValue];
                    if ([phone length] > 0) {
                        [contact.phones addObject:phone];
                    }
                }
            }
        }
    }        
}];

Also to get all contacts you can use the enumerateContactsWithFetchRequest method:

CNContactStore *store = [[CNContactStore alloc] init];
[store requestAccessForEntityType:CNEntityTypeContacts completionHandler:^(BOOL granted, NSError * _Nullable error) {
    if (granted == YES) {
        //keys with fetching properties
        NSArray *keys = @[CNContactFamilyNameKey, CNContactGivenNameKey, CNContactPhoneNumbersKey, CNContactImageDataKey];
        CNContactFetchRequest *request = [[CNContactFetchRequest alloc] initWithKeysToFetch:keys];
        NSError *error;
        BOOL success = [store enumerateContactsWithFetchRequest:request error:&error usingBlock:^(CNContact * __nonnull contact, BOOL * __nonnull stop) {
            if (error) {
                NSLog(@"error fetching contacts %@", error);
            } else {
                // copy data to my custom Contact class. 
                Contact *newContact = [[Contact alloc] init];
                newContact.firstName = contact.givenName;
                newContact.lastName = contact.familyName;
                // etc.
            }
        }];
    }        
}];

If you want to filter contacts by name you can use this:

Obj-C:

// keys from example above
NSArray *keys = @[CNContactFamilyNameKey, CNContactGivenNameKey, CNContactPhoneNumbersKey, CNContactImageDataKey];
NSArray *cnContacts = [store unifiedContactsMatchingPredicate:[CNContact predicateForContactsMatchingName:@"John Appleseed"] keysToFetch:keys error:&error];

Swift 3:

let store = CNContactStore()
let contacts = try store.unifiedContactsMatchingPredicate(CNContact.predicateForContactsMatchingName("Appleseed"), keysToFetch:[CNContactGivenNameKey, CNContactFamilyNameKey])

Official documentation is here: https://developer.apple.com/reference/contacts

Using Swift and Contacts framework to fetch all contacts, including name and phone numbers

import Contacts

let store = CNContactStore()
store.requestAccessForEntityType(.Contacts, completionHandler: {
    granted, error in

    guard granted else {
        let alert = UIAlertController(title: "Can't access contact", message: "Please go to Settings -> MyApp to enable contact permission", preferredStyle: .Alert)
        alert.addAction(UIAlertAction(title: "OK", style: .Default, handler: nil))
        self.presentViewController(alert, animated: true, completion: nil)
        return
    }

    let keysToFetch = [CNContactFormatter.descriptorForRequiredKeysForStyle(.FullName), CNContactPhoneNumbersKey]
    let request = CNContactFetchRequest(keysToFetch: keysToFetch)
    var cnContacts = [CNContact]()

    do {
        try store.enumerateContactsWithFetchRequest(request){
            (contact, cursor) -> Void in
            cnContacts.append(contact)
        }
    } catch let error {
        NSLog("Fetch contact error: \(error)")
    }

    NSLog(">>>> Contact list:")
    for contact in cnContacts {
        let fullName = CNContactFormatter.stringFromContact(contact, style: .FullName) ?? "No Name"
        NSLog("\(fullName): \(contact.phoneNumbers.description)")
    }
})

Fetching contact is slow operation, so you should not block main UI thread. Do CNContactFetchRequest on background thread. That's why I put the code into completionHandler. It's run on a background thread.