Dietary fibers contribute to structure and storage reserves of plant foods and fundamentally impact human health, partly by involving the intestinal microbiota, notably in the colon. Considerable attention has been given to unraveling the interaction between fiber type and gut microbiota utilization, focusing mainly on single, purified fibers. Studying these fibers in isolation might give us insights into specific fiber effects, but neglects how dietary fibers are consumed daily and impact our digestive tract: as intrinsic structures that include the cell matrix and content of plant tissues. Like our ancestors we consume fibers that are entangled in a complex network of plants cell walls that further encapsulate and shield intra-cellular fibers, such as fructans and other components from immediate breakdown. Hence, the physiological behavior and consequent microbial breakdown of these intrinsic fibers differs from that of single, purified fibers, potentially entailing unexplored health effects. In this mini-review we explain the difference between intrinsic and isolated fibers and discuss their differential impact on digestion. Subsequently, we elaborate on how food processing influences intrinsic fiber structure and summarize available human intervention studies that used intrinsic fibers to assess gut microbiota modulation and related health outcomes. Finally, we explore current research gaps and consequences of the intrinsic plant tissue structure for future research. We postulate that instead of further processing our already (extensively) processed foods to create new products, we should minimize this processing and exploit the intrinsic health benefits that are associated with the original cell matrix of plant tissues.