What's the best way to store Phone number in Django models

You might actually look into the internationally standardized format E.164, recommended by Twilio for example (who have a service and an API for sending SMS or phone-calls via REST requests).

This is likely to be the most universal way to store phone numbers, in particular if you have international numbers work with.

1. Phone by PhoneNumberField

You can use phonenumber_field library. It is port of Google's libphonenumber library, which powers Android's phone number handling https://github.com/stefanfoulis/django-phonenumber-field

In model:

from phonenumber_field.modelfields import PhoneNumberField

class Client(models.Model, Importable):
    phone = PhoneNumberField(null=False, blank=False, unique=True)

In form:

from phonenumber_field.formfields import PhoneNumberField
class ClientForm(forms.Form):
    phone = PhoneNumberField()

Get phone as string from object field:

    client.phone.as_e164 

Normolize phone string (for tests and other staff):

    from phonenumber_field.phonenumber import PhoneNumber
    phone = PhoneNumber.from_string(phone_number=raw_phone, region='RU').as_e164

2. Phone by regexp

One note for your model: E.164 numbers have a max character length of 15.

To validate, you can employ some combination of formatting and then attempting to contact the number immediately to verify.

I believe I used something like the following on my django project:

class ReceiverForm(forms.ModelForm):
    phone_number = forms.RegexField(regex=r'^\+?1?\d{9,15}$', 
                                error_message = ("Phone number must be entered in the format: '+999999999'. Up to 15 digits allowed."))

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EDIT

It appears that this post has been useful to some folks, and it seems worth it to integrate the comment below into a more full-fledged answer. As per jpotter6, you can do something like the following on your models as well:

models.py:

from django.core.validators import RegexValidator

class PhoneModel(models.Model):
    ...
    phone_regex = RegexValidator(regex=r'^\+?1?\d{9,15}$', message="Phone number must be entered in the format: '+999999999'. Up to 15 digits allowed.")
    phone_number = models.CharField(validators=[phone_regex], max_length=17, blank=True) # validators should be a list

Use django-phonenumber-field: https://github.com/stefanfoulis/django-phonenumber-field

pip install django-phonenumber-field

Use CharField for phone field in the model and the localflavor app for form validation:

https://docs.djangoproject.com/en/1.7/topics/localflavor/