Coming of Age for Horava Gravity: from Renormalizability to Black Holes

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After giving
an overview of the basic features of Horava gravity, I will focus on the latest developments and argue that, at least for the most general and complete version of the theory, the infrared phenomenology is by now relatively well understood and pathologies have been tamed. This implies that time has come for the theory to face a new series of intriguing challenges, related to quantization, ultraviolet phenomenology, black holes and singularities etc. I will present some ideas and first results in some of these directions.