Convergent evolutionary analogies (homoplasies) of many kinds occur in diverse phylogenetic clades/lineages on both the animal and plant branches of the Tree of Life. Living organisms whose last common ancestors lived millions to hundreds of millions of years ago have later converged morphologically, behaviorally or at other levels of functionality (from molecular genetics through biochemistry, physiology and other organismic processes) as a result of long term strong natural selection that has constrained and channeled evolutionary processes. This happens most often when organisms belonging to different clades occupy ecological niches, habitats or environments sharing major characteristics that select for a relatively narrow range of organismic properties. Systems biology, broadly defined, provides theoretical and methodological approaches that are beginning to make it possible to answer a perennial evolutionary biological question relating to convergent homoplasies: Are at least some of the apparent analogies actually unrecognized homologies? This review provides an overview of the current state of knowledge of important aspects of this topic area. It also provides a resource describing many homoplasies that may be fruitful subjects for systems biological research.