Our recent high-resolution laser spectroscopy of the Q(v)(0) (nu = nu <-- 0, J = 0 <-- 0) transitions in solid parahydrogen is discussed. The systems studied include the fundamental vibrational bands of impurity D2 and HD, the first and second overtones of parahydrogen, and the charge-induced spectrum of gamma-ray irradiated parahydrogen. Additionally, Stark and stimulated Raman-gain spectroscopies are applied to the solid. The linewidths are as sharp as 2 MHz HWHM, which is highly unusual for a solid. Our spectra demonstrate a variety of physical phenomena, particularly the deltak = 0 selection rule, as well as J = 1/J = 0 pair intermolecular interactions.