Cricket runs and maintains their own network. They also have Unlimited roaming agreements with MetroPCS and around 16 other regional partners to provide service for their customers in additional markets.
In areas where they do not provide service, Cricket customers can roam on Verizon (with Unlimited text messaging and a variable amount of minutes) as long as they are on the appropriate rate plan. Cricket's $50 rate plan for instance gives you 30 minutes of roaming on Verizon per month. Their $60 plan offers 200 minutes of Nationwide roaming.
Most of the largest markets in the US though are well covered by the Cricket/MetroPCS combination.