The growing interest in unmanned aerial vehicles (UAV) can be attributed to many factors, particularly the potential for them to operate beyond visual line of sight and at increasingly higher levels of autonomy. Trajectory planning defines the extent to which a vehicle is “autonomous”, therefore, to operate at high levels of autonomy, UAV will require real-time embedded trajectory planning that respects a minimum of flyability. This paper presents a review of recent advances in UAV trajectory planning and seeks to clarify the flyability, the real-time, and the embedded aspects, which are not adequately considered by previous survey papers. This work, which specifically focuses on Class II (≥150 and ≤600 kg) and Class III (>600 kg) fixed-wing UAV, analyses 60 papers from the last decade that mention some real-time achievement with respect to UAV trajectory planning. From this analysis, we highlight some challenges and some suggested orientations for future works.