About the removal of componentWillReceiveProps: you should be able to handle its uses with a combination of getDerivedStateFromProps and componentDidUpdate, see the React blog post for example migrations. And yes, the object returned by getDerivedStateFromProps updates the state similarly to an object passed to setState.

In case you really need the old value of a prop, you can always cache it in your state with something like this:

state = {
  cachedSomeProp: null
  // ... rest of initial state
};

static getDerivedStateFromProps(nextProps, prevState) {
  // do things with nextProps.someProp and prevState.cachedSomeProp
  return {
    cachedSomeProp: nextProps.someProp,
    // ... other derived state properties
  };
}

Anything that doesn't affect the state can be put in componentDidUpdate, and there's even a getSnapshotBeforeUpdate for very low-level stuff.

UPDATE: To get a feel for the new (and old) lifecycle methods, the react-lifecycle-visualizer package may be helpful.

As we recently posted on the React blog, in the vast majority of cases you don't need getDerivedStateFromProps at all.

If you just want to compute some derived data, either:

1. Do it right inside render
2. Or, if re-calculating it is expensive, use a memoization helper like memoize-one.

Here's the simplest "after" example:

import memoize from "memoize-one";

class ExampleComponent extends React.Component {
  getDerivedData = memoize(computeDerivedState);

  render() {
    const derivedData = this.getDerivedData(this.props.someValue);
    // ...
  }
}

Check out this section of the blog post to learn more.

As mentioned by Dan Abramov

Do it right inside render

We actually use that approach with memoise one for any kind of proxying props to state calculations.

Our code looks this way

// ./decorators/memoized.js  
import memoizeOne from 'memoize-one';

export function memoized(target, key, descriptor) {
  descriptor.value = memoizeOne(descriptor.value);
  return descriptor;
}

// ./components/exampleComponent.js
import React from 'react';
import { memoized } from 'src/decorators';

class ExampleComponent extends React.Component {
  buildValuesFromProps() {
    const {
      watchedProp1,
      watchedProp2,
      watchedProp3,
      watchedProp4,
      watchedProp5,
    } = this.props
    return {
      value1: buildValue1(watchedProp1, watchedProp2),
      value2: buildValue2(watchedProp1, watchedProp3, watchedProp5),
      value3: buildValue3(watchedProp3, watchedProp4, watchedProp5),
    }
  }

  @memoized
  buildValue1(watchedProp1, watchedProp2) {
    return ...;
  }

  @memoized
  buildValue2(watchedProp1, watchedProp3, watchedProp5) {
    return ...;
  }

  @memoized
  buildValue3(watchedProp3, watchedProp4, watchedProp5) {
    return ...;
  }

  render() {
    const {
      value1,
      value2,
      value3
    } = this.buildValuesFromProps();

    return (
      <div>
        <Component1 value={value1}>
        <Component2 value={value2}>
        <Component3 value={value3}>
      </div>
    );
  }
}

The benefits of it are that you don't need to code tons of comparison boilerplate inside getDerivedStateFromProps or componentWillReceiveProps and you can skip copy-paste initialization inside a constructor.

NOTE:

This approach is used only for proxying the props to state, in case you have some inner state logic it still needs to be handled in component lifecycles.