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Reanimated

react-native-reanimated provides an API that greatly simplifies the process of creating smooth, powerful, and maintainable animations. From the project's README:
It provides a more comprehensive, low level abstraction for the Animated library API to be built on top of and hence allow for much greater flexibility especially when it comes to gesture based interactions.

Platform Compatibility

Android DeviceAndroid EmulatoriOS DeviceiOS SimulatorWeb
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Installation

expo install react-native-reanimated

To use this in a bare React Native app, follow the installation instructions.

API Usage

You should refer to the react-native-reanimated docs for more information on the API and its usage. But the following example (courtesy of that repo) is a quick way to get started.
import React from 'react';
import { StyleSheet, Text, View, Button } from 'react-native';

import Animated, { Easing } from 'react-native-reanimated';

const { Value, timing } = Animated;

export default class Example extends React.Component {
  constructor(props) {
    super(props);
    this._transX = new Value(0);
    this._config = {
      duration: 5000,
      toValue: 180,
      easing: Easing.inOut(Easing.ease),
    };
    this._anim = timing(this._transX, this._config);
  }

  render() {
    return (
      <View style={styles.container}>
        <Animated.View style={[styles.box, { transform: [{ translateX: this._transX }] }]} />
        <Button
          onPress={() => {
            this._anim.start();
          }}
          title="Start"
        />
      </View>
    );
  }
}
const styles = StyleSheet.create({
  container: {
    flex: 1,
    justifyContent: 'center',
    backgroundColor: '#ecf0f1',
    padding: 8,
  },
  box: {
    width: 50,
    height: 50,
    backgroundColor: 'purple',
    borderRadius: 5,
  },
});