If you have experimented with op amp circuits at moderate gain and frequency, you probably have noted very good agreement between actual performance and ideal performance. As gain and/or frequency are increased, however, certain op amp limitations come into play that effect circuit performance.
In theory, with proper understanding of the internal structures and processes used to fabricate an op amp, we could calculate these effects. Thankfully this is not necessary, as manufacturers provide this information in data sheets. Proper interpretation of data sheet specifications is required when selecting an op amp for an application.
This discussion of op amp parameters is based on Texas Instruments’ data sheets. The following definitions (except as noted) are from the "Operational Amplifier Glossary" found in Texas Instruments’ data book, Amplifiers, Comparators, and Special Functions, pg. 1-37 to pg. 1-40 and pg. 5-37 to pg. 5-40. It defines most of the parameters found in the data sheets.