Deep learning is emerging in many industrial sectors in hand with big data analytics to streamline production. In the biomanufacturing sector, big data infrastructure is lagging comparatively to other industries. A promising approach is to combine Deep Neural Networks (DNN) with prior knowledge in Hybrid Neural Network (HNN) workflows that are less dependent on the quality and quantity of data. This paper reviews published articles over the past 30 years on the topic of HNN applications to bioprocesses. It revealed that HNNs were applied to various bioprocesses, including microbial cultures, animal cells cultures, mixed microbial cultures, and enzyme biocatalysis. HNNs were mainly applied for process analysis, process monitoring, development of software sensors, open- and closed-loop control, batch-to-batch control, model predictive control, intensified design of experiments, quality-by-design, and recently for the development of digital twins. Most previous HNN studies combined shallow Feedforward Neural Networks (FFNNs) with physical laws, such as macroscopic material balance equations, following the semiparametric design principle. Only recently, deep HNNs based on deep FFNNs, Convolution Neural Networks (CNN), Long Short-Term Memory (LSTM) networks and Physics Informed Neural Networks (PINNs) have been reported. The biopharma sector is currently a major driver but applications to biologics quality attributes, new modalities, and downstream processing are significant research gaps.