Can I host images in heroku? Or do I need S3?

The short answer: if you allow users or admins to upload images, you should not use Heroku's file system for this as the images will suddenly vanish.

As explained in the Heroku documentation:

Each dyno gets its own ephemeral filesystem, with a fresh copy of the most recently deployed code. During the dyno’s lifetime its running processes can use the filesystem as a temporary scratchpad, but no files that are written are visible to processes in any other dyno and any files written will be discarded the moment the dyno is stopped or restarted.

This means that user uploaded images on the Heroku filesystem are not only wiped out with every push, but also with every dyno restart, which occasionally happens (even if you would ping them frequently to prevent them going to sleep).

Once you start using a second web dyno, it will not be able to read the other dyno's filesystem, so then images would only be visible from one dyno. This would cause weird issues where users can sometimes see images and sometimes they don't.

That said, you can temporarily store images on the Heroku filesystem if you implement a pass-through file upload to an external file store.

Asset Pipeline

FiveDigit's answer is very good - there is something more to consider; the role of the asset pipeline in Rails

If the images you have are used as assets (IE they are used in the layout; are not changeable by the user), then you can store them in the assets/images folder. There is no limit to the number of assets you can keep with your application, but you must be sure on what these are - they are files which aid your application's operation; not files which can be uploaded / manipulated:

The asset pipeline provides a framework to concatenate and minify or compress JavaScript and CSS assets. It also adds the ability to write these assets in other languages and pre-processors such as CoffeeScript, Sass and ERB.

The asset pipeline will compress & fingerprint the stylesheet, image and js files it has, when you deploy your application to the likes of Heroku, or any other server. This means if those files don't change, you can store them in there

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S3

The reason you'd want to use the likes of S3 is specifically if your images files are designed to change (user can upload / edit them). Regardless of Heroku's filesystem, if the images are tied to changes in the DB, you'll have to keep a central store for them - if you change servers, they need to be reachable

To do this, you should ensure you appreciate how you want the files to work - are they going to be manipulated constantly by the user or not? If so, you'll have to explore integrating S3 into your app