Ion cyclotron emission (ICE) is detected from all large toroidal magnetically conned fusion (MCF) plasmas. It is a form of spontaneous suprathermal radiation, whose spectral peak frequencies correspond to sequential cyclotron harmonics of energetic ion species, evaluated at the emission location. We first present an account of the worldwide experimental ICE database, highlighting the phenomenological importance of the value of the ratio of energetic ion velocity v_Energetic to the local Alfvén speed V_A. We then focus on ICE measurements from heliotron-stellarator hydrogen plasmas, heated by energetic proton neutral beam injection (NBI) in the Large Helical Device, for which v_Energetic/V-A takes values both larger (super-Alfvénic) and smaller (sub-Alfvénic) than unity. The collective relaxation of the NBI proton population, together with the thermal plasma, is studied using a particle-in-cell (PIC) code. This evolves the Maxwell-Lorentz system of equations for hundreds of millions of kinetic gyro-orbit-resolved ions and fluid electrons, self-consistently with the electric and magnetic fields. For LHD-relevant parameter sets, the spatiotemporal Fourier transforms of the fields yield, in the nonlinear saturated regime, good computational proxies for the observed ICE spectra in both the super-Alfvénic and sub-Alfvénic regimes for NBI protons. At early times in the PIC treatment, the computed growth rates correspond to analytical linear growth rates of the magnetoacoustic cyclotron instability (MCI), which was previously identied to underly ICE from tokamak plasmas. The spatially localised PIC treatment does not include toroidal effects or geometry. Its success in simulating ICE spectra from both tokamak and, here, heliotron-stellarator plasmas suggests that the plasma parameters and ion energetic distribution at the emission location suffice to determine the ICE phenomenology. The capability to span the super-Alfvénic and sub-Alfvénic energetic ion regimes is a generic challenge in interpreting MCF plasma physics, and it is encouraging that this first principles computational treatment of ICE has now achieved this.