We present state-of-the-art computational methods which are instrumental in autonomous maritime operations, and optimization of routing, scheduling as well as loading. Our aim is to survey mature algorithmic approaches developed within the Lab of Geometric and Algebraic Algorithms, towards exploiting intelligence and automation in modern shipping and, in particular, in various aspects of routing. We showcase our advances in two main axes: (a) geometric computing for collision avoidance in complex environments, thus allowing for semi-autonomous and fully autonomous navigation, and (b) optimization for routing under time constraints of the carrier ship, time windows of availability at the ports of call, and capacity constraints of various compartments within a vessel.