I assume that you have some sort of List component and some sort of Item component. The way I did it in one project was to let the item know if it was active or not; the item would ask the list to scroll it into view if necessary. Consider the following pseudocode:

class List extends React.Component {
  render() {
    return <div>{this.props.items.map(this.renderItem)}</div>;
  }

  renderItem(item) {
    return <Item key={item.id} item={item}
                 active={item.id === this.props.activeId}
                 scrollIntoView={this.scrollElementIntoViewIfNeeded} />
  }

  scrollElementIntoViewIfNeeded(domNode) {
    var containerDomNode = React.findDOMNode(this);
    // Determine if `domNode` fully fits inside `containerDomNode`.
    // If not, set the container's scrollTop appropriately.
  }
}

class Item extends React.Component {
  render() {
    return <div>something...</div>;
  }

  componentDidMount() {
    this.ensureVisible();
  }

  componentDidUpdate() {
    this.ensureVisible();
  }

  ensureVisible() {
    if (this.props.active) {
      this.props.scrollIntoView(React.findDOMNode(this));
    }
  }
}

A better solution is probably to make the list responsible for scrolling the item into view (without the item being aware that it's even in a list). To do so, you could add a ref attribute to a certain item and find it with that:

class List extends React.Component {
  render() {
    return <div>{this.props.items.map(this.renderItem)}</div>;
  }

  renderItem(item) {
    var active = item.id === this.props.activeId;
    var props = {
      key: item.id,
      item: item,
      active: active
    };
    if (active) {
      props.ref = "activeItem";
    }
    return <Item {...props} />
  }

  componentDidUpdate(prevProps) {
    // only scroll into view if the active item changed last render
    if (this.props.activeId !== prevProps.activeId) {
      this.ensureActiveItemVisible();
    }
  }

  ensureActiveItemVisible() {
    var itemComponent = this.refs.activeItem;
    if (itemComponent) {
      var domNode = React.findDOMNode(itemComponent);
      this.scrollElementIntoViewIfNeeded(domNode);
    }
  }

  scrollElementIntoViewIfNeeded(domNode) {
    var containerDomNode = React.findDOMNode(this);
    // Determine if `domNode` fully fits inside `containerDomNode`.
    // If not, set the container's scrollTop appropriately.
  }
}

If you don't want to do the math to determine if the item is visible inside the list node, you could use the DOM method scrollIntoView() or the Webkit-specific scrollIntoViewIfNeeded, which has a polyfill available so you can use it in non-Webkit browsers.

For React 16, the correct answer is different from earlier answers:

class Something extends Component {
  constructor(props) {
    super(props);
    this.boxRef = React.createRef();
  }

  render() {
    return (
      <div ref={this.boxRef} />
    );
  }
}

Then to scroll, just add (after constructor):

componentDidMount() {
  if (this.props.active) { // whatever your test might be
    this.boxRef.current.scrollIntoView();
  }
}

Note: You must use '.current,' and you can send options to scrollIntoView:

scrollIntoView({
  behavior: 'smooth',
  block: 'center',
  inline: 'center',
});

(Found at http://www.albertgao.xyz/2018/06/07/scroll-a-not-in-view-component-into-the-view-using-react/)

Reading the spec, it was a little hard to suss out the meaning of block and inline, but after playing with it, I found that for a vertical scrolling list, block: 'end' made sure the element was visible without artificially scrolling the top of my content off the viewport. With 'center', an element near the bottom would be slid up too far and empty space appeared below it. But my container is a flex parent with justify: 'stretch' so that may affect the behavior. I didn't dig too much further. Elements with overflow hidden will impact how the scrollIntoView acts, so you'll probably have to experiment on your own.

My application has a parent that must be in view and if a child is selected, it then also scrolls into view. This worked well since parent DidMount happens before child's DidMount, so it scrolls to the parent, then when the active child is rendered, scrolls further to bring that one in view.

Another example which uses function in ref rather than string

class List extends React.Component {
  constructor(props) {
    super(props);
    this.state = { items:[], index: 0 };
    this._nodes = new Map();

    this.handleAdd = this.handleAdd.bind(this);
    this.handleRemove = this.handleRemove.bind(this);
   }

  handleAdd() {
    let startNumber = 0;
    if (this.state.items.length) {
      startNumber = this.state.items[this.state.items.length - 1];
    }

    let newItems = this.state.items.splice(0);
    for (let i = startNumber; i < startNumber + 100; i++) {
      newItems.push(i);
    }

    this.setState({ items: newItems });
  }

  handleRemove() {
    this.setState({ items: this.state.items.slice(1) });
  }

  handleShow(i) {
    this.setState({index: i});
    const node = this._nodes.get(i);
    console.log(this._nodes);
    if (node) {
      ReactDOM.findDOMNode(node).scrollIntoView({block: 'end', behavior: 'smooth'});
    }
  }

  render() {
    return(
      <div>
        <ul>{this.state.items.map((item, i) => (<Item key={i} ref={(element) => this._nodes.set(i, element)}>{item}</Item>))}</ul>
        <button onClick={this.handleShow.bind(this, 0)}>0</button>
        <button onClick={this.handleShow.bind(this, 50)}>50</button>
        <button onClick={this.handleShow.bind(this, 99)}>99</button>
        <button onClick={this.handleAdd}>Add</button>
        <button onClick={this.handleRemove}>Remove</button>
        {this.state.index}
      </div>
    );
  }
}

class Item extends React.Component
{
  render() {
    return (<li ref={ element => this.listItem = element }>
      {this.props.children}
    </li>);
  }
}

Demo: https://codepen.io/anon/pen/XpqJVe