While you can view all Stripe transactions on your Stripe Dashboard, you can also view your payments and payouts by navigating to System > Settings > Payment Integrations > Card Payments with Stripe > Payments.
An example of the Stripe Account Payments page.
Here you have two tabs: Payments and Payouts. The Payments tab records all payments received from Clients, while the 'Payouts' tab helps you monitor all the payouts you have received from Stripe. Moreover, you can click the little download arrow next to the payment/payout to download a spreadsheet containing a list of payments included in it.
Alongside this, if you'd like to export the Stripe payments feed, you can click on the export button highlighted below and download the CSV file within your desired date range.
Exporting the Stripe Feed.