Increasingly, academics have to demonstrate that their research has academic impact. Universities normally use journal rankings and journal impact factors to assess the research impact of individual academics. More recently, citation counts for individual articles and the h-index have also been used to measure the academic impact of academics. There are, however, several serious problems with relying on journal rankings, journal impact factors and citation counts. For example, articles without any impact may be published in highly ranked journals or journals with high impact factor, whereas articles with high impact could be published in lower ranked journals or journals with low impact factor. Citation counts can also be easily gamed and manipulated, and the h-index disadvantages early career academics. This paper discusses these and several other problems and suggests alternatives such as post-publication peer review and open-access journals.