Doctrine Cache does the job but by implementing a standard the Symfony Cache seems to have another advantage besides its delievered anyway. So i checked it out.

Documentation is still a bit sparse and the best resource so far is this blogpost:
https://symfony.com/blog/new-in-symfony-3-1-cache-component

I wont go into detail on how you use the Cache but rather how you integrate it with Redis, which is my favourite Cache backend.

You can create a Cache service via the FrameworkBundle in your config.yml and you can also create a default Redis client to use with your Cache service.

framework:
    default_locale: de
    secret: ThisTokenIsNotSoSecretChangeIt
    assets: ~
    templating:
        engines: ['twig']
    cache:
	default_redis_provider: "redis://%cache.redis_host%:%cache.redis_port%/%cache:redis_db%"
        pools:
           sf_cache:
             adapter: cache.adapter.redis
             public: true
             default_lifetime: 1200
             provider: cache.default_redis_provider

When the Redis Extension is present it will use the extension elsewards it will use Predis, which is plain PHP.
You can also pass any other client. F.e. if you have already created a Predis client service in your app then just pass this as provider.

    cache:
        pools:
           sf_cache:
             adapter: cache.adapter.redis
             public: true
             default_lifetime: 1200
             provider: my.predis.client.service.id

I recently discovered SncRedisBundle and i have to say i like it :)
I used to create Predis clients directly because its very easy and thought i wouldnt need a bundle for this.
But with SncRedisBundle you get Logging and WebProfiler support additionally, which is great for development.
Also you get some more easy symfony integrations for other stuff as Doctrine, Mailings or Sessions which i dont use but maybe you do.
So check it out.

So my best move is to use SncRedisBundle to create a Redis client and integrate it with the Cache Component.

snc_redis:
    clients:
        sf_cache:
            type: predis
            alias: sf_cache
            dsn: "redis://%cache.redis_host%:%cache.redis_port%/0"
            logging: "%kernel.debug%"

framework:
    default_locale: de
    secret: ThisTokenIsNotSoSecretChangeIt
    assets: ~
    templating:
        engines: ['twig']
    cache:
        pools:
           sf_cache:
             adapter: cache.adapter.redis
             public: true
             default_lifetime: 1200
             provider: snc_redis.sf_cache

Now you have integrated caching with webprofiler appearance and logging, nice!

UPDATE
You can also add your snc redis client to the standard app cache, provided with symfony:

cache:
    prefix_seed: my-app
    app: cache.adapter.redis
    system: cache.adapter.redis
    default_redis_provider: snc_redis.cache

alright, do so by:

open:
/etc/redis/redis.conf

you will find:

#   Note: you can disable saving at all commenting all the "save" lines.

save 900 1
save 300 10
save 60 10000

do as you are told:

#save 900 1
#save 300 10
#save 60 10000

…and save.
then restart redis.

sudo /etc/init.d/redis-server restart

Doing!