What to use in place of ::ng-deep

The simple and easy alternative to a deep style is a common style using the element selector of the parent component. So if you had this in hero-details.component.css:

:host ::ng-deep h3 {
  font-style: italic;
}

It would become this in styles.css:

app-hero-details h3 {
  font-style: italic;
}

Basically a deep style is an un-encapsulated style so it conceptually seems more like a common style to me than a component style. Personally I would not use deep styles anymore. Breaking changes are normal in major version updates and deprecated feature removal is fair game.

To bypass the deprecated ::ng-deep, I usually disable ViewEncapsulation. Although this is not the best approach, it has served me well.

To disable ViewEncapsulation, do the following in your component:

import { Component, ViewEncapsulation } from '@angular/core';

@Component({
  selector: 'app-header',
  templateUrl: './header.component.html',
  styleUrls: ['./header.component.scss'],
  encapsulation: ViewEncapsulation.None
})

export class HeaderComponent {

}

This will make the .scss styles in this component global to the whole application. To not allow the styles to go up the chain to parent and sibling components, wrap the whole scss with the selector like so:

app-header {
  // your styles here and any child component styles can go here
}

Now, the styles specified here will go down to children components so you have to be extra specific with your css selectors and mind your p's and q's when adding CSS (maybe add the child selector specified in your Angular app and then its styles).

I say it is not the best approach because of the paragraph above, but this has served me well.

FWIW In my research I have not found any replacement for ng-deep or the other applicable alternatives. This is because, I believe, the Angular team is deferring to the W3C spec on the shadow dom, which initially had selectors such as deep. However, the W3c has since removed the recommendation, but not replaced it with a new one. Until that happens, I imagine that the Angular team will keep ::ng-deep and it's alternatives available, but in deprecated state due to the pending state of W3C's drafts. I am not able to take the time to find the documentation to back this up right now but I did see it recently.

Long story short: Keep using ::ng-deep and its alternatives until a replacement is created - the deprecation is just an early notice so that people aren't blindsided whenever the actual change materializes.

-- UPDATE --

https://drafts.csswg.org/css-scoping-1/ Here is the draft proposal if you're interested. It appears that they are working on a robust set of selectors for elements within a shadow dom tree; it is this spec, once approved, that I think will inform the angular clone, if there even is one (i.e. angular may not need to implement their own selectors once this goes live in browsers).