How to set current user to user field in Django Rest Framework?

It depends on your use case. If you want it to be "write-only", meaning DRF automatically populates the field on write and doesn't return the User on read, the most straight-forward implementation according to the docs would be with a HiddenField:

class PhotoListAPIView(generics.ListCreateAPIView):
    user = serializers.HiddenField(
        default=serializers.CurrentUserDefault(),
    )

If you want want it to be readable, you could use a PrimaryKeyRelatedField while being careful that your serializer pre-populates the field on write - otherwise a user could set the user field pointing to some other random User.

class PhotoListAPIView(generics.ListCreateAPIView):
    user = serializers.PrimaryKeyRelatedField(
        # set it to read_only as we're handling the writing part ourselves
        read_only=True,
    )

    def perform_create(self, serializer):
        serializer.save(user=self.request.user)

Finally, note that if you're using the more verbose APIView instead of generics.ListCreateAPIView, you have to overwrite create instead of perform_create like so:

class PhotoListAPIView(generics.ListCreateAPIView):
    user = serializers.PrimaryKeyRelatedField(
        read_only=True,
    )

    def create(self, validated_data):
        # add the current User to the validated_data dict and call
        # the super method which basically only creates a model
        # instance with that data
        validated_data['user'] = self.request.user
        return super(PhotoListAPIView, self).create(validated_data)

You can avoid passing the user in your request and you won't see it in the output but DRF will populate it automatically:

from rest_framework import serializers

class MyModelSerializer(serializers.ModelSerializer):
    user = serializers.HiddenField(default=serializers.CurrentUserDefault())

    class Meta:
        model = models.MyModel
        fields = (
            'user',
            'other',
            'fields',
        )

You can use CurrentUserDefault:

user = serializers.PrimaryKeyRelatedField(
    read_only=True, 
    default=serializers.CurrentUserDefault()
)

Off the top of my head, you can just override the perform_create() method:

class PhotoListAPIView(generics.ListCreateAPIView):
    ...
    def perform_create(self, serializer):
        serializer.save(user=self.request.user)

Give that a shot and let me know if it works