Reflecting our experiences in areas, like Algebraic Specifications, Abstract Model Theory, Graph Transformations, and Model Driven Software Engineering (MDSE), we present a general, category independent approach to Logics of First-Order Constraints (LFOC). Traditional First-Order Logic, Description Logic and the sketch framework are discussed as examples. We use the concept of institution [Diaconescu08,GoguenBurstall92] as a guideline to describe LFOC's. The main result states that any choice of the six parameters, we are going to describe, gives us a corresponding "institution of constraints" at hand. The "presentations" for an institution of constraints can be characterized as "first-order sketches". As a corresponding variant of the "sketch-entailments" in [Makkai97], we finally introduce "sketch rules" to equip LFOC's with the necessary expressive power.