Will I need a visa to travel to the EU post Brexit?

No, if you hold a passport from an EU member state. UK passport holders will not need a visa to travel to Ireland or the Continent for trips of up to 90 days however the continuation of this arrangement is dependant on further negotiations. The same applies vice versa: holders of Irish and other EU passports do not need a visa to travel to the UK. Here you can obtain general information on passports before your journey:

https://www.gov.uk/browse/abroad/passports 

The above Q&A is based on latest government advice which may be subject to change.