If you are the family member of an EU citizen and you yourself are from a non-EU country, you can apply for a Residence Card for Family Members of EU Citizens.
BUT: This used to apply only in case of spouses and children of the EU citizen or their spouse. Parents of EU citizens were only covered if they depended on their children in every way, more than anything economically. So, only the parents of adult EU citizens could get the EU Family Member Residence Card and only in case the dependency could be proven (which is very difficult).
Parents of minor EU citizens did not fall under the EU Regime. The only option they had in Spain was to apply for an extraordinary residence permit called "Arraigo Familiar". This permit has many disadvantages compared to the EU Family Residence Permit and to refer the parents to this permit was to ignore their family relationship with an EU citizen as well as its importance.
Now, FINALLY, non-EU parents of EU minors can apply for their very own Residence Cards for Family Members of EU Citizens, or EU Family Permit. This card will last them 5 years and they can renew it afterwards as a permanent residence permit.
In order to apply for the EU Family Permit for parents, they have to show sufficient economic means, health insurance and the family relationship. In case of parents of Spaniards, they do not have to show sufficient economic means. In case the parent/s do not have an income and do not dispose of other means, they can still apply for "Arraigo Familiar".