Frequency and bandwith of Op-amp
Frequency compensation is added to opamps to make them 'unity gain stable'.

Slow (micro-power) compensated amps might have a GBW of 50kHz. Fast compensated ones are available with GBW > 1GHz. So the fact that it's compensated does not directly relate to speed choices.

As so many people use opamps as voltage followers, or in other circuits with low or unity gain (integrators, peak detectors), the manufacturers do us the service of making most opamps available in form that's stable if you simply connect the output back to the -ve input, so they are easy to use without doing stability calculations. So many opamps are available in this form, and many types only available in this form, that few users realise that this is an option.

The 'bombproof' frequency compensation that's added to opamps is called 'dominant pole compensation', one (to misquote Lord of the Rings) time constant to rule them all. This gives them a gain that falls at 6dB per octave, and so a 90 degree phase shift, all the way down to below unity gain, before other poles begin to bite and increase the phase shift. So pretty much nothing the user can do accidentally when making an amplifier will make them oscillate (you can still deliberately make an oscillator if you want).

This gives a compensated amplifier a well defined GBW, gain bandwidth product. If the gain crosses unity at 10MHz, then you can get gain of 10 at 1MHz, gain of 100 at 100kHz etc.

If built to a 'natural' design, any given multi-stage high gain amplifier will tend have a gain that drops faster than 6dB per octave before we cross unity gain. As the various devices in it 'run out of steam' at high frequency, each will contribute its own pole, and the phase shift from the several poles will increase beyond 180 degrees while there is still significant gain. This amplifier is not unity gain stable, and will oscillate if connected as a follower.

Compensating an amplifier with a single dominant pole does restrict the gain and hence speed of any given amplifier. Some amplifiers are available uncompensated, for users who understand the stability limitations and have the skill to work with them. Generally, a gain higher than unity is required to use such an amplifier. 

Given two amplifiers in different technologies, a fast unity gain stable one, and a slower uncompensated one, the latter can do a gain of 10 amplifier in the same bandwidth with less power than the former. 

Given two amplifiers in the same technology with different degrees of compensation, the uncompensated one will have a higher slew rate, and more gain at high frequencies.

Check out this family of high speed opamps that are identical except for their internal compensation for different minimum gains.