The new concept of nuclear tidal waves allows one to calculate the sequence of states with maximal angular momentum (yrast states). These states correspond to a surface wave running around the nucleus as tidal waves run over the earth's oceans. Such a wave corresponds to a static deformation in the rotating frame of reference, which allows one to calculate its properties by means of the microscopic cranking model. There exists a large group of transitional nuclei that show a behavior between harmonic vibration and rotation, a description of which has been a long-standing challenge to nuclear theory. The new concept of nuclear tidal waves allows one to calculate the sequence of states with maximal angular momentum (yrast states).