Let's consider two servers -- named "one" and "two". Server "one" has the following tags. Server "two" has no tags.

Get tags for server "one".

devstack@devstack:~/devstack$ curl -H "X-Auth-Token: $MY_TOKEN" -H "X-Openstack-Nova-API-Version: 2.60" http://127.0.0.1/compute/v2.1/servers/74d6e8ae-9ad3-48e5-9591-f4fb2054606b/tags -X GET
{"tags": ["blue", "green", "red"]}



tags=blue returns "one"

devstack@devstack:~/devstack$ curl -H "X-Auth-Token: $MY_TOKEN" -H "X-Openstack-Nova-API-Version: 2.60" http://127.0.0.1/compute/v2.1/servers?tags=blue -X GET | python -mjson.tool
{
    "servers": [
        {
            "id": "74d6e8ae-9ad3-48e5-9591-f4fb2054606b",
            "links": [
                {
                    "href": "http://127.0.0.1/compute/v2.1/servers/74d6e8ae-9ad3-48e5-9591-f4fb2054606b",
                    "rel": "self"
                },
                {
                    "href": "http://127.0.0.1/compute/servers/74d6e8ae-9ad3-48e5-9591-f4fb2054606b",
                    "rel": "bookmark"
                }
            ],
            "name": "one"
        }
    ]
}



tags-any=blue also returns "one"

devstack@devstack:~/devstack$ curl -H "X-Auth-Token: $MY_TOKEN" -H "X-Openstack-Nova-API-Version: 2.60" http://127.0.0.1/compute/v2.1/servers?tags-any=blue -X GET | python -mjson.tool
{
    "servers": [
        {
            "id": "74d6e8ae-9ad3-48e5-9591-f4fb2054606b",
            "links": [
                {
                    "href": "http://127.0.0.1/compute/v2.1/servers/74d6e8ae-9ad3-48e5-9591-f4fb2054606b",
                    "rel": "self"
                },
                {
                    "href": "http://127.0.0.1/compute/servers/74d6e8ae-9ad3-48e5-9591-f4fb2054606b",
                    "rel": "bookmark"
                }
            ],
            "name": "one"
        }
    ]
}


tags=blue,teacup returns no servers.

devstack@devstack:~/devstack$ curl -H "X-Auth-Token: $MY_TOKEN" -H "X-Openstack-Nova-API-Version: 2.60" http://127.0.0.1/compute/v2.1/servers?tags=blue,teacup -X GET | python -mjson.tool
{
    "servers": []
}


tags-any=blue,teacup returns "one"

devstack@devstack:~/devstack$ curl -H "X-Auth-Token: $MY_TOKEN" -H "X-Openstack-Nova-API-Version: 2.60" http://127.0.0.1/compute/v2.1/servers?tags-any=blue,teacup -X GET | python -mjson.tool
{
    "servers": [
        {
            "id": "74d6e8ae-9ad3-48e5-9591-f4fb2054606b",
            "links": [
                {
                    "href": "http://127.0.0.1/compute/v2.1/servers/74d6e8ae-9ad3-48e5-9591-f4fb2054606b",
                    "rel": "self"
                },
                {
                    "href": "http://127.0.0.1/compute/servers/74d6e8ae-9ad3-48e5-9591-f4fb2054606b",
                    "rel": "bookmark"
                }
            ],
            "name": "one"
        }
    ]
}


not-tags=blue,teacup returns "one" and "two"

devstack@devstack:~/devstack$ curl -H "X-Auth-Token: $MY_TOKEN" -H "X-Openstack-Nova-API-Version: 2.60" http://127.0.0.1/compute/v2.1/servers?not-tags=blue,teacup -X GET | python -mjson.tool
{
    "servers": [
        {
            "id": "af3e60f5-cfa4-4be0-be6b-5144bfbfee12",
            "links": [
                {
                    "href": "http://127.0.0.1/compute/v2.1/servers/af3e60f5-cfa4-4be0-be6b-5144bfbfee12",
                    "rel": "self"
                },
                {
                    "href": "http://127.0.0.1/compute/servers/af3e60f5-cfa4-4be0-be6b-5144bfbfee12",
                    "rel": "bookmark"
                }
            ],
            "name": "two"
        },
        {
            "id": "74d6e8ae-9ad3-48e5-9591-f4fb2054606b",
            "links": [
                {
                    "href": "http://127.0.0.1/compute/v2.1/servers/74d6e8ae-9ad3-48e5-9591-f4fb2054606b",
                    "rel": "self"
                },
                {
                    "href": "http://127.0.0.1/compute/servers/74d6e8ae-9ad3-48e5-9591-f4fb2054606b",
                    "rel": "bookmark"
                }
            ],
            "name": "one"
        }
    ]
}


not-tags-any=blue,teacup returns "two"

devstack@devstack:~/devstack$ curl -H "X-Auth-Token: $MY_TOKEN" -H "X-Openstack-Nova-API-Version: 2.60" http://127.0.0.1/compute/v2.1/servers?not-tags-any=blue,teacup -X GET | python -mjson.tool
{
    "servers": [
        {
            "id": "af3e60f5-cfa4-4be0-be6b-5144bfbfee12",
            "links": [
                {
                    "href": "http://127.0.0.1/compute/v2.1/servers/af3e60f5-cfa4-4be0-be6b-5144bfbfee12",
                    "rel": "self"
                },
                {
                    "href": "http://127.0.0.1/compute/servers/af3e60f5-cfa4-4be0-be6b-5144bfbfee12",
                    "rel": "bookmark"
                }
            ],
            "name": "two"
        }
    ]
}