Most organic compounds provide vibrational spectra within the CH stretching region, yet the signal is difficult to interpret because of multiple difficulties in experiment and modeling. To better understand various factors involved, the ability of several harmonic and anharmonic computational approaches to describe these vibrations was explored for α-pinene, fenchone, and camphor as test compounds. Raman, Raman optical activity (ROA), infrared absorption (IR), and vibrational circular dichroism (VCD) spectra were measured and compared to quantum chemical computations. Surprisingly, the harmonic vibrational approach reasonably well reproduced the measured spectral patterns, including the vibrational optical activity (VOA). The CH stretching, however, appeared to be more sensitive to the basis set and solvent variations than lower-frequency vibrations. For a higher accuracy in frequencies and spectral shapes, anharmonic corrections were necessary. Accurate harmonic and anharmonic force fields were obtained with the mPW2PLYP double-hybrid functional. A limited vibrational configuration interaction (LVCI) where the CH stretching motion was decoupled from other vibrations provided the best simulated spectra. A balanced harmonic oscillator basis set had to be used, containing also states indirectly interacting with fundamental vibrations. A simpler second-order perturbational approach (PT2) appeared less useful. The modeling provided unprecedented agreement with experimental vibrational frequencies; spectral shapes were reproduced less faithfully. The possibility of ab initio interpretation of the CH spectral region for relatively large molecules further broadens the application span of vibrational spectroscopy.