The way our brain learns to disentangle complex signals into unambiguous concepts is fascinating but remains largely unknown. There is evidence, however, that hierarchical neural representations play a key role in the cortex. This thesis investigates biologically plausible models of unsupervised learning of hierarchical representations as found in the brain and modern computer vision models. We use computational modeling to address three main questions at the intersection of artificial intelligence (AI) and computational neuroscience. The first question is: What are useful neural representations and when are deep hierarchical representations needed? We approach this point with a systematic study of biologically plausible unsupervised feature learning in a shallow 2-layer networks on digit (MNIST) and object (CIFAR10) classification. Surprisingly, random features support high performance, especially for large hidden layers. When combined with localized receptive fields, random feature networks approach the performance of supervised backpropagation on MNIST, but not on CIFAR10. We suggest that future models of biologically plausible learning should outperform such random feature benchmarks on MNIST, or that such models should be evaluated in different ways. The second question is: How can hierarchical representations be learned with mechanisms supported by neuroscientific evidence? We cover this question by proposing a unifying Hebbian model, inspired by common models of V1 simple and complex cells based on unsupervised sparse coding and temporal invariance learning. In shallow 2-layer networks, our model reproduces learning of simple and complex cell receptive fields, as found in V1. In deeper networks, we stack multiple layers of Hebbian learning but find that it does not yield hierarchical representations of increasing usefulness. From this, we hypothesise that standard Hebbian rules are too constrained to build increasingly useful representations, as observed in higher areas of the visual cortex or deep artificial neural networks. The third question is: Can AI inspire learning models that build deep representations and are still biologically plausible? We address this question by proposing a learning rule that takes inspiration from neuroscience and recent advances in self-supervised deep learning. The proposed rule is Hebbian, i.e. only depends on pre- and post-synaptic neuronal activity, but includes additional local factors, namely predictive dendritic input and widely broadcasted modulation factors. Algorithmically, this rule applies self-supervised contrastive predictive learning to a causal, biological setting using saccades. We find that networks trained with this generalised Hebbian rule build deep hierarchical representations of images, speech and video. We see our modeling as a potential starting point for both, new hypotheses, that can be tested experimentally, and novel AI models that could benefit from added biological realism.