In the first part of the paper, we study the collapse of flexible highly charged polyelectrolyte chains induced by attractive dipole-dipole interactions. The latter emerge due to the formation of dipoles between the chain monomers and counterions condensed on the polyelectrolyte from solution. Using the statistics of slightly perturbed Gaussian polymers, we obtain the scaling relations for the chain dimensions as a function of polyelectrolyte linear charge density in the limit of compacting chains. The results are in good agreement with the outcomes of recent molecular dynamics simulations of the collapse of flexible polyelectrolytes in the presence of explicit counterions. In the second part, we analyze the results of molecular dynamics simulations for the complex formation by two highly charged polyelectrolyte chains carrying opposite charges. We use the scaling arguments based on the picture of complexation of electrostatic blobs in order to rationalize the size of the complexes of two polyelectrolyte chains in the collapsed state. Similar scaling relation for the complex size was recently obtained in computer simulations of complexation of diblock polyampholytes and was described theoretically on the basis of similar electrostatic blob concepts. We also analyze the density of complexes formed and polyelectrolyte linear charge densities required for the onset onto the collapse as a function of interaction strength between the monomers. In both parts of the paper, we overview the scaling relationships obtained for similar systems with alternating charges from other theoretical approaches.