High-precision processing of materials with ultrafast laser pulses is drawing increasing attention as laser sources are finally catching up with industry requirements. In particular, very rapid progress has been achieved in ultrafast fiber lasers, which are popular as a result of their highly repeatable, environmentally robust performance, compact size and possibility to reach high average powers. Meanwhile, our understanding of the rich physics of ultrafast laser-material interaction remains incomplete, wherein lies new opportunities. A particularly exciting possibility concerns the use of groups of pulses, which are extremely closed in time. This changes the interaction physics drastically: A unqualified increase in laser repetition rate would result in severe heat accumulation and other undesirable effects. The average power can be kept at a desirable level by operating the laser in the so-called burst mode, whereby each burst contains a number of closely spaced pulses, benefiting from accumulative effects, while the bursts are repeated at much lower repetition rate. Under the right conditions, including keeping average power low enough to prevent excessive heat accumulation, relatively low peak powers for which plasma shielding and similar effects are reduced, ultrafast burst mode can lead to an order-of-magnitude increases in processing speed compared to uniform repetition rate operation of an otherwise identical laser source.