Recently, the performance of blind speech separation (BSS) and target speech extraction (TSE) has greatly progressed. Most works, however, focus on relatively well-controlled conditions using, e.g., read speech. The performance may degrade in more realistic situations. One of the factors causing such degradation may be intrinsic speaker variability, such as emotions, occurring commonly in realistic speech. In this paper, we investigate the influence of emotions on TSE and BSS. We create a new test dataset of emotional mixtures for the evaluation of TSE and BSS. This dataset combines LibriSpeech and Ryerson Audio-Visual Database of Emotional Speech and Song (RAVDESS). Through controlled experiments, we can analyze the impact of different emotions on the performance of BSS and TSE. We observe that BSS is relatively robust to emotions, while TSE, which requires identifying and extracting the speech of a target speaker, is much more sensitive to emotions. On comparative speaker verification experiments we show that identifying the target speaker may be particularly challenging when dealing with emotional speech. Using our findings, we outline potential future directions that could improve the robustness of BSS and TSE systems toward emotional speech.