We provide an overview of the rapidly evolving landscape of integrated photonic neuromorphic architectures, specifically targeting the implementation of convolutional neural networks. The exploding research momentum stems from the well-known advantages of photonic circuits compared to digital electronics, and at the same time, it is driven by the massive need for cognitive image/video processing. In this context, we provide a detailed literature review on photonic cores operating as convolutional neural networks, covering either the functionality of a conventional neural network or its spiking counterpart. Moreover, we propose 2 alternative photonic approaches that refrain from simply transferring neural network concepts directly into the optical domain; instead, they focus on fusing photonic, digital electronic, and event-based bioinspired processing to optimally exploit the virtues of each scheme. These approaches can offer beyond state-of-the-art performance while relying on realistic, scalable technology. The first approach is based on a photonic integrated platform and a bioinspired spectrum-slicing technique. The photonic chip allows feature extraction through optical filtering with low power consumption and an equivalent computational efficiency of 72 femtojoules per multiply-and-accumulate operation for 5-bit precision. When combined with typical digital neural networks, an almost 5-fold reduction in the number of parameters was achieved with a minor loss of accuracy compared to established convolutional neural networks. The second approach follows a bioisomorphic route in which miniaturized spiking laser neurons and unsupervised bioinspired training are unified in a deep architecture, revealing a noise-resilient and power-efficient proposition.