This dissertation investigates the frontoparietal ‘multiple-demand’ (MD) network that is involved in the processing of diverse cognitive demands. This network is active when the task at hand is made more demanding, in a variety of different tasks including working memory, task switching, inhibition, math, language etc. While the different MD regions have partly different functions, they are highly interconnected allowing them to function together as a network. The experiment in Chapter 2 looked at the interplay between functional differences as well as co-recruitment within this multiple-demand network. Quantitative differences between regions were more prominent in simple tasks. A strong co-recruitment was seen with increased challenge or incentive. In Chapter 3, task preferences were studied at the voxel level. MD regions were equally well localised in single-subjects using any of three task demands. Voxels localised by all three tasks also captured the underlying neural representations to a similar level in a separate criterion task. Chapter 4 investigated if task representations, as measured by multi-voxel patterns, were modified due to external motivation. The effect was limited to the cue phase and did not extend to the stimulus processing phase where the stimulus is integrated with the cue to arrive at the response. Chapter 5 examined neural representations in frontal and parietal regions more directly through single unit activity and local field potentials (LFPs), during a spatial working memory task. While single neurons showed dynamic coding of target information rather than persistent coding, LFPs held this information constant through time. The impact of reference voltages on LFP data was further investigated. Together, these results explore the functional differences between and within the MD regions, and provide evidence for flexible task representations at the voxel and neuronal level.