I Introduction: Assignment Criteria.- 1. Transition energy.- 2. Oscillator strength.- 3. Transition moment direction.- 4. Magnetic circular dichroism.- 5. Substituent effects.- 6. Less general criteria.- II Experimental Techniques.- 1. The stretched sheet method.- 2. Electric fields.- 3. Magnetic fields.- 4. Hydrodynamic shear.- 5. Crystal methods.- 6. Liquid crystal methods.- 7. Photoselection.- III Interpretation of the Observed Spectra.- 1. Vibronic interactions.- 2. Interpretation of LD-spectra. Absolute moment directions.- 3. The description of a partially oriented uniaxial sample.- 4. Determination of reduced spectra for symmetrical molecules.- 5. The orientation triangle.- 6. Orientation models.- 7. Interpretation of LD-data for low symmetry molecules.- 8. Identical chromophores in different molecules.- 9. Non-uniaxial samples.- 10. Interpretation of MCD-spectra.- IV Theoretical Models.- 1. The ?-electron approximation.- 2. Semiempirical calculations.- 3. Calculation of MCD B-terms. Alternant hydrocarbons.- 4. MCD of derivatives of alternant hydrocarbons.- 5. Summary.- V Examples of LD and MCD Spectra and Spectral Assignments.- 1. Fluoranthene.- 2. Thiophene.- 3. Acenaphthylene.- 4. p-Terphenyl.- VI Conclusions.- 1. The assignment process.- 2. Interpretation of LD spectra.- 3. Theoretical descriptions of electronic transitions.- 4. New applications of MCD spectroscopy.- Acknowledgment.- References.