Based on Django Rest Framework's Filtering Documentation, there are two ways to access parameters from a request.

1. URL Params

If you are using URL params (such as mywebapp.com/api/<user_slug>/resource/), you can access the arguments like this: self.kwargs['param_name'] where param_name is the name of the parameter you're trying to get the value for. So for the example above, you'd have user_slug = self.kwargs['user_slug']

Example from the documentation

If your URL structure looks like this:

url('^purchases/(?P<username>.+)/$', PurchaseList.as_view()),

...and want to filter on that username. You can override the get_queryset() and your view will look like this:

class PurchaseList(generics.ListAPIView):
    serializer_class = PurchaseSerializer

    def get_queryset(self):
        """
        This view should return a list of all the purchases for
        the user as determined by the username portion of the URL.
        """
        username = self.kwargs['username']
        return Purchase.objects.filter(purchaser__username=username)

2. Query Params

If you are using query parameters such as mywebapp.com/api/resource?user_slug=plain-jane, you can use self.request to access request as you can in plain vanilla Django REST methods. This gives you access to things like self.request.query_params. For the example above, you would say user_slug = self.request.query_params['user_slug']. You can also access the current user like user = self.request.user.

Example from the documentation

Let's say you want to support a request structure like this:

http://example.com/api/purchases?username=denvercoder9

...and want to filter on that username. Do this to override the queryset:

class PurchaseList(generics.ListAPIView):
    serializer_class = PurchaseSerializer

    def get_queryset(self):
        """
        Optionally restricts the returned purchases to a given user,
        by filtering against a `username` query parameter in the URL.
        """
        queryset = Purchase.objects.all()
        username = self.request.query_params.get('username', None)
        if username is not None:
            queryset = queryset.filter(purchaser__username=username)
        return queryset

Django 2

Use request.parser_context

 def perform_create(self, serializer):
        post_id = self.request.parser_context['kwargs'].get('post_id')
        post = Post.objects.get(id=post_id)
        serializer.save(post=post)

adding a little to what they have already contributed, for the POST methods in modelviewset when an object is sent, it is necessary to use request.data['myvariable']

example:

class BoxViewSet(viewsets.ModelViewSet):

    queryset = Uploadobject.objects.all().exclude(verified=False)
    serializer_class = BoxSerializer
    permission_classes = (permissions.IsAuthenticatedOrReadOnly,
                        IsBox)

    def create(self, request):
       ...
       make = request.data['make']