We propose a theoretical framework for testing concurrent systems from true concurrency models like Petri nets or networks of automata. The underlying model of computation of such formalisms are labeled event structures, which allow to represent concurrency explicitly. The activity of testing relies on the definition of a conformance relation that depends on the observable behaviors on the system under test, which is given for sequential systems by ioco type relations. However, these relations are not capable of capturing and exploiting concurrency of non sequential behavior. We study different conformance relations for labeled event structures, relying on different notions of observation, and investigate their properties and connections.