Energetic ion-driven magnetohydrodynamic instabilities such as Alfvén eigenmodes (AEs), energetic particle modes (EPMs), and their impacts on energetic ion confinement are being studied on the Large Helical Device (LHD). The magnetic configuration of this device is three dimensional and has negative magnetic shear over a whole radial region in the low-beta regime. Two types of toroidicity-induced Alfvén eigenmodes (TAEs) are typically observed in LHD plasmas that are heated by tangential neutral beam injection: One is localized in the plasma core region near a central TAE gap and the other is a global TAE having a radially extended eigenfunction. Core-localized TAEs with even and odd radial mode parities are often observed. The global TAE is usually observed in medium- to high-beta plasmas where broad regions with low magnetic shear are present. Helicity-induced Alfvén eigenmodes (HAEs), which exist in gaps unique to three-dimensional plasmas that have both toroidal and poloidal mode couplings, were detected for the first time. Recently, reversed magnetic shear Alfvén eigenmodes (RSAEs) having characteristic frequency sweeping were discovered in reversed magnetic shear (RS) plasmas produced by intense counter-neutral beam current drive. In the RS plasma, the geodesic acoustic mode (GAM) excited by energetic ions, which is a global-type mode different from localized GAM excited by drift waves, was also detected for the first time in a helical plasma. Nonlinear couplings between RSAE and GAM modes and also between two TAEs were observed. Bursts of TAEs and EPMs often enhance radial transport and loss of energetic ions at low toroidal magnetic field (<0.75 T).