Continuous-Carbon-Fiber (CF)/polyaryletherketone (PAEK) composites have recently attracted interest especially in the aerospace industry due to short-time processes and possible weldability and recyclability. However, their manufacturing remains challenging as it involves several steps such as tape fabrication, tape lay-up and consolidation. This last step mainly aims at achieving a sufficiently low void content composite to obtain the desired mechanical properties. To become an economically viable alternative over classical thermoset-based composites, “in-situ” or out-of-autoclave (OOA) consolidation processes have to become part of the manufacturing process of CF/PAEK. These techniques have, for now, some limitations which lead to difficulties in producing parts of the same quality as autoclave consolidated ones. Understanding the multi-scale rheological phenomena involved during consolidation is therefore critical, which constitutes the main goal of this review. Reflecting on the literature, guides for improving the OOA and “in-situ” consolidation, both in terms of process and materials, are finally suggested.