I answered this question on the Quora question-answering site.
First, let’ define “undertaking”. That doesn’t mean that the vehicle is a hearse. It means that the vehicle passes between yours and the edge of the road when you are near the edge and turning toward it. Since the question mentions a left turn, the questioner is probably in a country where traffic keeps left by default and normally passes on the right. The term ‘undertake” is more commonly used in the British Isles than in North America in any case. But the question could apply to a left turn from the left side of a one-way street anywhere.
Usually, the driver who undertakes is at fault. Generally there is not room for another dual-track vehicle to pass between the turning vehicle and the edge of the roadway, though there may be room if more than one lane allows left turns, or room for a single-track vehicle (motorcycle, motorized bicycle, bicycle). A driver might also undertake on a highway shoulder or by driving off the road. In any of these cases, it is illegal.
Some countries place a bicycle lane or barrier-separated bikeway in the path of the turning traffic, and if the undertaking driver is a bicyclist, the turning driver is held at fault. The resulting conflict may be not mitigated at all, or mitigated in any of several ways — with warning signs, street geometry, street markings or traffic signals. The intention of this arrangement is to relieve bicyclists of the burden of mixing with motor traffic to travel straight through the intersection, and so, placing all of the responsibility for avoiding collisions on the motorist.
Because of the speed with which bicyclists travel, the turning driver is required to look to the rear to the side toward which he or she is turning, rather than only first merging to the lane position for the turn and then yielding to pedestrians who are standing on the corner or walking in the crosswalk. Looking to the rear imposes an additional task burden on the driver at a time where attention to the front and sides is also in demand, and may even be impossible, depending on the geometry of the intersection and the design of the turning vehicle. Unless drivers know to expect this conflict and mitigating factors are in place, this is a risky situation, often resulting in what is called in the USA a “right hook” collision. It also reduces the throughput of intersections by requiring additional waiting — sometimes by motorists, sometimes by bicyclists and sometimes by both.