The good news for travellers is that from April 2016 EU "Roaming" prices are going to drop considerably and as from June 2017 there will be no more roaming charges within the EU. Unfortunately this is not a world-wide decission so countries not in the European Union will continue to charge what they like. Currently phone companies are allowed to add 19 cents a minute to your outgoing calls, 5 cents aminute to incoming calls, 6 cents for a text message and 20 cents for ever MB of date used. In April 2016 those priceswill drop to 5 cent for calls, 2 cents for SMS and 5 cents per meg of data. Already a good deal. Then in June 2017 you pay the same in any EU country as you would back home.
The two main companies with their own system are Movistar and Vodofone/Ono. Both companies are installing their own fibre optic system to provide land-line speeds of up to 300MB. There's strict laws about setting up new telephone masts so currently almost all are owned by Movistar and the other companies are able to use them too. As far as landlines go, the other companies (other than Ono) all use Movistar.