The Local Universe is the most detail studied part of the observable region of space with the radius R about 100 Mpc. There are two empirical fundamental cosmological laws directly established from observations in the Local Universe independently from cosmological theory: first, the Hubble-Humason-Sandage linear redshift-distance law and second, Carpenter- Karachentsev-deVaucouleurs density-radius power-law. Review of modern state of these empirical laws and their cosmological significance is given. Possible theoretical interpretations of the surprising coexistence of both laws at the spatial scales from 1 Mpc to 100 Mpc are discussed. Comparison of the standard space-expansion explanation of the cosmological redshift with possible global gravitational redshift model is given.