A lot of people who have played final fantasy throughout the series have a fond love of the summoner class. There has been great speculation as to wether or not summoner would ever be possible to implement. Most people even doubted that dragoon would get a pet again. However, it appears that people can put their worries to rest, as a fighting pet system is planned to be implemented amongst the many changes to come.

"New summoning ability available to certain jobs and classes after version 2.0.
New taming ability available to certain jobs and classes after version 2.0. Summoned and tamed pets will not count as party members, and will develop over time. Release of a "companion" system for these pet NPCs to fight alongside PCs."
I remember literally seeing "Pets are impossible to implement in FFXIV". Well it seems that with a new system/server overhaul in place, anything is possible.

In Summary, pet summons will become available for jobs/classes after 2.0.

It's a LONG wait, but I remain confident that the changes will be well worth it and look forward at the chance of being able to call forth a companion in battle.