The European Parliament has been steadily gaining power over recent decades and now acts as a co-legislator for nearly all EU law. Together with the Council, the Parliament adopts or amends proposals from the Commission. Parliament also supervises the work of the Commission and adopts the European Union's budget. See how it all works here.
Beyond these official powers the Parliament also works closely with national parliaments of EU countries. Regular joint parliamentary assemblies allow for a better inclusion of national perspectives into the Parliament's deliberations.