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It is generally believed that modification of general relativity inevitably introduce extra physical degree(s) of freedom.
In this talk I argue that this is not the case by constructing modified gravity theories with two local physical degrees of freedom. After classifying such theories into two types, I show explicit examples and discuss their cosmology and phenomenology.

It was during his stay in Prague when Einstein started in earnest to develop his ideas about general relativity. I will evoke those days in 1911 and 1912, discuss Einstein's papers on gravitation from that period, emphasize which new concepts and ideas he introduced. I also want to show you how the main themes that preoccupied him then, the principle of equivalence, bending of light, gravitational redshift and frame dragging effects are still alive in contemporary relativity.