Microalgae are well known for their ability to accumulate lipids intracellularly, which can be used for biofuels and mitigate CO emissions. However, due to economic challenges, microalgae bioprocesses have maneuvered towards the simultaneous production of food, feed, fuel, and various high-value chemicals in a biorefinery concept. On-line and in-line monitoring of macromolecules such as lipids, proteins, carbohydrates, and high-value pigments will be more critical to maintain product quality and consistency for downstream processing in a biorefinery to maintain and valorize these markets. The main contribution of this review is to present current and prospective advances of on-line and in-line process analytical technology (PAT), with high-selectivity - the capability of monitoring several analytes simultaneously - in the interest of improving product quality, productivity, and process automation of a microalgal biorefinery. The high-selectivity PAT under consideration are mid-infrared (MIR), near-infrared (NIR), and Raman vibrational spectroscopies. The current review contains a critical assessment of these technologies in the context of recent advances in software and hardware in order to move microalgae production towards process automation through multivariate process control (MVPC) and software sensors trained on "big data". The paper will also include a comprehensive overview of off-line implementations of vibrational spectroscopy in microalgal research as it pertains to spectral interpretation and process automation to aid and motivate development.