Tumor development and progression is the consequence of genetic as well as epigenetic alterations of the cell. As part of the epigenetic regulatory system, histone acetyltransferases (HATs) and deacetylases (HDACs) drive the modification of histone as well as non-histone proteins. Derailed acetylation-mediated gene expression in cancer due to a delicate imbalance in HDAC expression can be reversed by histone deacetylase inhibitors (HDACi). Histone deacetylase inhibitors have far-reaching anticancer activities that include the induction of cell cycle arrest, the inhibition of angiogenesis, immunomodulatory responses, the inhibition of stress responses, increased generation of oxidative stress, activation of apoptosis, autophagy eliciting cell death, and even the regulation of non-coding RNA expression in malignant tumor cells. However, it remains an ongoing issue how tumor cells determine to respond to HDACi treatment by preferentially undergoing apoptosis or autophagy. In this review, we summarize HDACi-mediated mechanisms of action, particularly with respect to the induction of cell death. There is a keen interest in assessing suitable molecular factors allowing a prognosis of HDACi-mediated treatment. Addressing the results of our recent study, we highlight the role of p53 as a molecular switch driving HDACi-mediated cellular responses towards one of both types of cell death. These findings underline the importance to determine the mutational status of p53 for an effective outcome in HDACi-mediated tumor therapy.