Population-genetic studies have been remarkably productive and successful in the last decade following the invention of PCR technology and the introduction of mitochondrial and microsatellite DNA markers. While mitochondrial DNA has proven powerful for genealogical and evolutionary studies of animal populations, and microsatellite sequences are the most revealing DNA markers available so far for inferring population structure and dynamics, they both have important and unavoidable limitations. To obtain a fuller picture of the history and evolutionary potential of populations, genealogical data from nuclear loci are essential, and the inclusion of other nuclear markers, i.e. single copy nuclear polymorphic (scnp) sequences, is clearly needed. Four major uncertainties for nuclear DNA analyses of populations have been facing us, i.e. the availability of scnp markers for carrying out such analysis, technical laboratory hurdles for resolving haplotypes, difficulty in data analysis because of recombination, low divergence levels and intraspecific multifurcation evolution, and the utility of scnp markers for addressing population-genetic questions. In this review, we discuss the availability of highly polymorphic single copy DNA in the nuclear genome, describe patterns and rate of evolution of nuclear sequences, summarize past empirical and theoretical efforts to recover and analyse data from scnp markers, and examine the difficulties, challenges and opportunities faced in such studies. We show that although challenges still exist, the above-mentioned obstacles are now being removed. Recent advances in technology and increases in statistical power provide the prospect of nuclear DNA analyses becoming routine practice, allowing allele-discriminating characterization of scnp loci and microsatellite loci. This certainly will increase our ability to address more complex questions, and thereby the sophistication of genetic analyses of populations.