How to control docker-compose build order?

The accepted answer above does not seem correct.

As seen in the documentation

There are several things to be aware of when using depends_on:

depends_on does not wait for db and redis to be “ready” before starting web - only until they have been started. If you need to wait for a service to be ready, see Controlling startup order for more on this problem and strategies for solving it.

Version 3 no longer supports the condition form of depends_on.

The depends_on option is ignored when deploying a stack in swarm mode with a version 3 Compose file.

Update: In recent practice, I have found my answer to only pertain to run ordering.
Refer to the answer by Quinten Scheppermans and the comment by Authur Weborg about dobi.

You can control build order using depends_on directive.

services:
  ...

  B:
    depends_on:
      - A
  C:
    depends_on:
      - A

Since compose v2, BuildKit is enabled by default, it will build images parallelly.

By disabling BuildKit you get to build images according to the order in your docker-compose.yml file.

DOCKER_BUILDKIT=0 docker-compose build

If you still want to build images parallelly, you can consider defining services in multiple docker-compose.yml files for building, then composing up in another docker-compose.yml file for deployment.

If you need to run one service before an other you can use docker-compose run bar after setting depends_on: - foo in your docker-compose.yml file.

For example:

# docker-compose.yml

  services:
    foo:
        . . . 
    bar:
         . . . 
      depends_on:
        - foo

then run,

# terminal

user@Name Docker % docker-compose run bar

However, per the docs, this will only control the order in which processes start, not the order in which they finish. This can often lead to situations in which dependent services do not properly start. Potential solutions for this include using wait-for-it, wait-for, or Dockerise. I recommend reading the docs before implementing any of the solutions listed above, as there are caveats.

One thing that fixed a similar issue for me was the additional_contexts option added in version 2.17 of the Compose tool. So if derived/dockerfile has, for example,

COPY --from base-image /build/. /build/.

we can ensure that base-image is built first with a docker-compose that looks like this:

services:
    base:
        build:
            dockerfile: "base/dockerfile"
            context: .
        image: base-image
    derived:
        build:
            dockerfile: "derived/dockerfile"
            context: .
            additional_contexts:
                base-image: service:base

As stated in https://github.com/docker/compose/blob/e9220f45df07c1f884d5d496507778d2cd4a1687/compose/project.py#L182-L183

Preserves the original order of self.services where possible, reordering as needed to resolve dependencies.

So for me it worked by manually sorting the services with the depending services at first and following the services which is used by the other and the other as last.

Example

version: '3'
services:
    mydb:
        image: mydb
    serviceA:
        build: 
            dockerfile: DockerfileA
        depends_on:
            - mydb
    serviceB:
        build:
            dockerfile: DockerfileB # which contains 'FROM serviceA'
        depends_on:
            - mydb

Source: https://github.com/docker/compose/issues/5228#issuecomment-565469948