Sr2RuO4 is a paradigmatic unconventional superconductor. Despite the tremendous efforts made in the past twenty-seven years, the exact nature of its superconductivity is still controversial. To date, no superconducting state conceivable for this material seems able to interpret in a coherent manner the numerous key experimental observations. Our research on the theory of Sr2RuO4 began in 2011 and continues till this date, and our work covers both phenomenological and microscopic aspects.  The most recent studies are summarized in this review. Some representative publications on this subject are listed below.

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