This work reviews recent advances in technologies for functional magnetic resonance imaging (fMRI) of the human brain and highlights the push for higher functional specificity based on increased spatial resolution and specific MR contrasts to reveal previously undetectable functional properties of small-scale cortical structures. We discuss how the combination of MR hardware, advanced acquisition techniques and various MR contrast mechanisms have enabled recent progress in functional neuroimaging. However, these advanced fMRI practices have only been applied to a handful of neuroscience questions to date, with the majority of the neuroscience community still using conventional imaging techniques. We thus discuss upcoming challenges and possibilities for fMRI technology development in human neuroscience. We hope that readers interested in functional brain imaging acquire an understanding of current and novel developments and potential future applications, even if they don't have a background in MR physics or engineering. We summarize the capabilities of standard fMRI acquisition schemes with pointers to relevant literature and comprehensive reviews and introduce more recent developments.