This paper presents calculations of optical harmonic spectra for atoms and ions in the high intensity regime relevant to current short-pulse experiments. It shows that ions can produce harmonics comparable in strength to those from neutrals and that their emission extends to much higher orders. Simple scaling laws for harmonic emission strength and maximum observable harmonic are suggested. These results imply that recent experiments in helium and neon contain contributions from ions as well as neutrals. When an atom is exposed to an intense laser field, it develops a time-dependent dipole moment and radiates at odd multiples of the incident laser frequency. This process, known as optical harmonic generation (OHG), has been studied at low to moderate intensities. However, current laser systems can produce intensities up to $10^{17}$ W/cm². Recent experiments have observed high-order harmonic generation in rare gases at intensities beyond the saturation intensity for the atom and its ionization stages. These experiments probe the limits of OHG, possibly for ions as well. The results show that ions can emit very high-order harmonics with magnitudes comparable to those from neutrals. The emission from ions extends to much higher orders than from neutrals. The paper also presents a simple formula to estimate the maximum observable harmonic photon for given experimental conditions. It shows that the maximum harmonic is given by $E_{max} \approx I_p + 3U_p$, where $U_p = I/4\omega^2$ is the ponderomotive shift of the ionization potential. The paper also discusses the scaling of harmonic intensities with laser intensity and the role of ions in harmonic generation. It shows that the height of the plateau in harmonic spectra is proportional to the ionization rate. The results suggest that systems with the lowest excited state as far as possible above the ground state produce the maximum number of harmonics. The paper concludes that ions can contribute significantly to harmonic spectra in the intensity regime of current experiments. However, the contributions from ions can become competitive with those from neutrals only when the peak intensity in the focal volume experienced by the ions equals or exceeds their saturation intensity. At such intensities, it is difficult to determine experimentally the source of the photoemission because the observed signal is phase matched over a macroscopic distance, and both species are present in the focal volume. The paper also discusses the effects of free electrons on high-order harmonics, which are more deleterious at longer incident wavelengths.This paper presents calculations of optical harmonic spectra for atoms and ions in the high intensity regime relevant to current short-pulse experiments. It shows that ions can produce harmonics comparable in strength to those from neutrals and that their emission extends to much higher orders. Simple scaling laws for harmonic emission strength and maximum observable harmonic are suggested. These results imply that recent experiments in helium and neon contain contributions from ions as well as neutrals. When an atom is exposed to an intense laser field, it develops a time-dependent dipole moment and radiates at odd multiples of the incident laser frequency. This process, known as optical harmonic generation (OHG), has been studied at low to moderate intensities. However, current laser systems can produce intensities up to $10^{17}$ W/cm². Recent experiments have observed high-order harmonic generation in rare gases at intensities beyond the saturation intensity for the atom and its ionization stages. These experiments probe the limits of OHG, possibly for ions as well. The results show that ions can emit very high-order harmonics with magnitudes comparable to those from neutrals. The emission from ions extends to much higher orders than from neutrals. The paper also presents a simple formula to estimate the maximum observable harmonic photon for given experimental conditions. It shows that the maximum harmonic is given by $E_{max} \approx I_p + 3U_p$, where $U_p = I/4\omega^2$ is the ponderomotive shift of the ionization potential. The paper also discusses the scaling of harmonic intensities with laser intensity and the role of ions in harmonic generation. It shows that the height of the plateau in harmonic spectra is proportional to the ionization rate. The results suggest that systems with the lowest excited state as far as possible above the ground state produce the maximum number of harmonics. The paper concludes that ions can contribute significantly to harmonic spectra in the intensity regime of current experiments. However, the contributions from ions can become competitive with those from neutrals only when the peak intensity in the focal volume experienced by the ions equals or exceeds their saturation intensity. At such intensities, it is difficult to determine experimentally the source of the photoemission because the observed signal is phase matched over a macroscopic distance, and both species are present in the focal volume. The paper also discusses the effects of free electrons on high-order harmonics, which are more deleterious at longer incident wavelengths.