You may have already noticed on the right section of the site, that there's a box that follows you everywhere where you could be interested in placing a bet.
It contains two tabs, Single: where you manage your un-opened bets and Open Bets: where you can see your opened bets, Matched or Unmatched.
Originally Betslip has this aspect:
If you click on some odds to bet, the Betslip would be automatically updated with the chosen selections on the Single Tab:
If you confirm your bets from Single Tab and the system accepts them, they will be acceped and would be visible from the Open Bets Tab
Please note that a bet followed by the green check icon means is was already matched
The Betslip will filter, group and also only show your bets related to the market / event you are currently in. If you want to see your detailed betting activity you should go to My Account -> My Bets