In this article, the leader-following exponential consensus problem of fractional-order descriptor multiagent systems (FOD-MASs) with event-triggered control (ETC) protocol is investigated, which includes integer-order descriptor multiagent systems as the special case. Two classes of control schemes and the corresponding event-triggered conditions are presented, respectively. First, a distributed state feedback ETC protocol is developed to reach the leader-following exponential consensus. The leader-following exponential consensus is achieved in the sense of the Mittag-Leffler stability of fractional-order systems. Second, when full-state measurements are not available, a novel observer-type output feedback ETC strategy with some desirable characteristics is provided. For two distributed ETC protocols, consensus conditions are derived and convergence rate of the system can be adjusted. Also, the integral inequality is applied to get the fact that Zeno behavior is excluded, which verifies the feasibility of ETC schemes. Finally, the effectiveness of conclusions is demonstrated by the examples.