In this talk I would like to give an overview of several projects that I am coordinating where different fields of mathematics are being applied in the fishing and maritime industries. First, we will see how data science and Machine Learning can be used to develop models that are able to interpret echosounder data collected by Fish Aggregating Devices (FADs) and other oceanographic variables to estimate the size of a tuna school under a FAD. This model, called Tuna-AI, can in turn be used for several purposes such as describing patterns of tuna behavior or developing abundance indices and other tasks related to sustainability of tuna fisheries. Next, we will see how mathematical optimization of different flavors can be used to improve merchant shipping routes, using fine-grained oceanographic and weather data, and taking into account the dynamic nature of the problem. This is part of a project called Smart Shipping (see here), that has already won a prize at the 2021 Ocean Hackathon. We would like to conclude with some open problems as part of our future research agenda, such as solving the decision problem for a fishing vessel that visits FADs and sets until it reaches the assigned quota of catches. Time permitting, I will briefly touch upon other applied projects that involve natural language processing and computer vision applied to healthcare: monitoring of newborn babies and automatic structuring of clinical reports. The takeaway message, illustrated by means of these real examples, is that mathematical techniques can improve the efficiency of standard practices in many industries. But also, and perhaps more surprisingly, that applied problems can also motivate and trigger novel and challenging problems for fundamental research.