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Golay sequence pairs have been applied in multislit spectrometry, optical time domain reflectometry, multicarrier wireless transmission, and medical ultrasound. They are closely related to Barker sequences and Reed-Muller codes. In 1990, Eliahou, Kervaire and Saffari used a polynomial formulation to constrain the possible length of a Golay sequence pair; no further general nonexistence results have been found. 3-phase Golay sequence triads were introduced by Frank in 1980, but have since been largely neglected even though they are particularly suited to practical implementation. I shall describe constructions for infinite families of 3-phase Golay sequence triads, and discuss numerical results suggesting these triads have a much richer existence pattern than the more familiar Golay sequence pairs. I shall outline an elementary argument giving the first general nonexistence result for 3-phase Golay sequence triads. This is joint work with Aki Avis.