In contrast to random diffusion without orientation, chemotaxis is the biased movement of biological entities toward the region that contains higher concentration of beneficial or lower concentration of unfavorable chemicals. The former often refers to as chemo-attraction and the latter as chemo-repulsion. Chemotaxis has been advocated as a leading mechanism to account for the morphogenesis and self-organization of a variety of biological coherent structures such as aggregates, fruiting bodies, clusters, spirals, spots, rings, labyrinthine patterns and stripes. This talk is built on a sequence of past and recent results on the qualitative analysis of systems of balance laws arising from chemotaxis models with logarithmic sensitivity. Specifically, we focus on the long-time asymptotic behavior of classical solutions to the PDE models with naturally prepared initial data and subject to steady and evolutionary boundary conditions of Dirichlet and Neumann type. Some open problems will also be discussed.