adjective
BAD : The current world encourages creativity.
GOOD : The modern world encourages creativity.
BAD : We need to know current English, not the language of Shakespeare.
GOOD : We need to know modern English, not the language of Shakespeare.
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current = happening or existing now, but not likely to last for a long time: 'How long has she been going out with her current boyfriend?' 'The current boom in long-haul travel has led to fierce competition among the major airlines.'
modern = used or existing in the period of history that we live in now, and not in an earlier period: 'What do you think of modern architecture?' 'Even by modern standards, the pyramids are a remarkable piece of engineering.'