What TypeScript type should I use to reference the match object in my props?

To add onto @Nazar554's answer above, the RouteComponentProps type should be imported from react-router-dom, and implemented as follows.

import {BrowserRouter as Router, Route, RouteComponentProps } from 'react-router-dom';

interface MatchParams {
    name: string;
}

interface MatchProps extends RouteComponentProps<MatchParams> {
}

Further, to allow for re-usable components, the render() function allows you to pass only what the component needs, rather than the entire RouteComponentProps.

<Route path="/products/:name" render={( {match}: MatchProps) => (
    <ProductContainer name={match.params.name} /> )} />

// Now Product container takes a `string`, rather than a `MatchProps`
// This allows us to use ProductContainer elsewhere, in a non-router setting!
const ProductContainer = ( {name}: string ) => {
     return (<h1>Product Container Named: {name}</h1>)
}

You don't need to add it explicitly. You can use RouteComponentProps<P> from @types/react-router as a base interface of your props instead. P is type of your match params.

import { RouteComponentProps } from 'react-router';

// example route
<Route path="/products/:name" component={ProductContainer} />

interface MatchParams {
    name: string;
}

interface Props extends RouteComponentProps<MatchParams> {
}

// from typings
import * as H from "history";

export interface RouteComponentProps<P> {
  match: match<P>;
  location: H.Location;
  history: H.History;
  staticContext?: any;
}

export interface match<P> {
  params: P;
  isExact: boolean;
  path: string;
  url: string;
}