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In recent years there have been a significant progress in the study of spatial organization and in vivo dynamics of chromosome matter both in procaryotic and eucaryotic cells. Understanding the various experimental results obtained in this field is closely related, from theoretical physics point of view, with the study of the dense but unenentangled states of polymer chains, such as melts of nonconcatenated polymer rings, and the so-called fractal globule state of polymer chains, as well as the study of polymer chain dynamics surrounded by active and/or viscoelastic media. I present some novel results in the field, in particular I will discuss the generalization of classical Rouse model of polymer dynamics for fractal unentangled polymer conformations with spatial fractal exponent df different from 2 (in particular, df = 3 for the fractal globule). Also, I show how this model can be generalized for a polymer in a viscoelastic medium where probe particle undergoes a fractal Brownian motion with a given Hurst exponent H. A scaling theory for spatial-temporal correlation functions of such polymer conformations will be also presented, and the possible comparisons with available and future experimental data will be discussed.