The paper aims at investigating the interactions between a floating wave energy device (WEC) and its mooring system under a variety of wave conditions (regular and irregular, perpendicular and oblique, ordinary and extreme). The analyzed WEC is the DEXA, a wave activated body point absorber, of the type that performs better when aligned to the incident wave direction. Two typologies of mooring systems were studied: for limited depths, the spread system, with a disposition of the lines that do not constrain the yaw movements; for large depths, the catenary anchor leg mooring (CALM) system. The spread system was experimentally investigated, including a realistic power take-off system, to capture non-linear behaviors and assess device motions, power production, and forces on mooring lines. The CALM system was numerically simulated, as mooring modelling is more reliable in deep waters and allows testing of a number of different configurations, by changing the number of the mooring lines and the mooring layout. The experiments showed that a reduction of the mooring compliancy increases the power production. The numerical simulations showed that a redundancy on the number of chains allows a better distribution of the loads, with advantages on reliability and costs.