Depending on the payment type you select, the invoices act differently.
Card Payments
If you have selected card payment as the payment type then invoices are not automatically sent to customers. Customers will have access to them in their account at any time, by selecting 'My account' on your storefront.
Manual Payments
Invoices are automatically sent for subscriptions using manual payment types, bank transfer, cash etc. However during the subscription creation process you can opt to turn off the 'invoice on renewal date'.
Changing Stripe Settings
You can choose to send invoices for all subscriptions by making a change in the Stripe settings. Select the settings cog in the top right then under 'Billing' select 'subscriptions and emails'. Scroll down to the 'Manage invoices sent to customers' section where you can turn on the ability to 'Send finalised invoices to customer'.