What are the roles of the co-pilot in commercial aviation?
Firstly, "co-pilot" is not a term that is really used anymore. When people say that they usually mean the First Officer. It's a bugbear of mine because "co-pilot" implies that there is one real pilot and a half pilot, when the reality is an airliner needs at least two fully qualified pilots to fly it safely! 

When it comes to actually flying the plane, the two pilots have designated roles - Pilot Flying (PF) and Pilot Monitoring (PM - sometimes this is called Pilot Not Flying). Both the Captain and the First Officer share these roles - usually one of them is PF on the outbound leg and the other one is PM on the inbound leg. The PF manipulates the controls to actually fly the plane, whereas the PM handles communications and other required tasks that don't involve actually flying the plane. 

The biggest difference between a Captain and a First officer is responsibility. The Captain is the Pilot In Command (PIC), who has ultimate responsibility for everything that happens throughout the flight. There are some practical things that only Captains can do, like flying into some tricky airports, landing in strong crosswinds, and on many aircraft only the Captain can use the steering wheel (or Tiller) for taxiing. 

Historically there was a strong heirarchy - the Captain was the boss and the co-pilot was, you could say, a servant. This posed big problems, because the Captain is not always right. The advent of Crew Resource Management (CRM) has brought this down to a much more desirable level - where there is still a heirarchy to ensure decisions are made, but not so much that they are unquestionable. The future of the First Officer role will be one of continuing to recognise that they play an important role in a functioning cockpit, rather than just there to serve the Captain. And hopefully people will stop calling them co-pilots!