Diversion of income earned to low tax jurisdictions

Dear Friends

Can the Income earned by a person/company be diverted to low tax jurisdictions?? 

For example, cayman islands, we all know it charges very low/nil taxes on incomes.

So, how will the income which is diverted away to such low tax jurisdicitions is taxed?? Also, what are the ways in which people divert their incomes??

Regards