Monetary systems are traditionally formed by the policy decisions of individual governments and administrated as a domestic economic issue.
The current trend, however, is to use international trade and investment to alter the policy and legislation of individual governments. The best recent example of this policy is the European Union's creation of the euro as a common currency for many of its individual states. Modern currencies are not linked to physical commodities (silver or gold) and are not a contract to deliver a good or service. As such the value of a currency fluctuates based on politics, perception and emotion in addition to monetary policy.
Apart from monetary systems based on money, there do also exist systems based on "favours". One example of this is the LETS system. LETS, or Local Exchange Trading Systems, are local community trading groups where members exchange their goods and services with each other.