1)What are the advantages of high compression?

2)What are the advantages of low compression?

3)If I where to build a motor; wanting torque and horse power.
a)how would a higher compression engine serve me?
b)how would a lower compression engine serve me?

4)Regardless of whether this engine was used for street/strip or towing. What the advantages or disadvantages of both?

All input is appreciated.

Robert P.