To see your order history, you will need to create an account and log in. It is best to do this before you checkout, so you will benefit from Race Reward Points, but you can create an account after you have made your order.
Your order history is available by visiting the website here and clicking on Order History, or clicking the avatar icon on the website (top right). You can also see your Race Reward Points, Gift Vouchers, and update your communication preferences.