Why is Natural Language Processing interesting? What makes NLP hard? How can we bring NLP research to practice? These are all open-ended questions. In this talk, I present a novel approach called selectional branching, which optimizes both accuracy and speed for one of core NLP tasks, dependency parsing. Our approach uses confidence estimates to decide when to employ a beam, providing the accuracy of beam search at speeds close to a greedy dependency parsing approach. Selectional branching is guaranteed to perform faster than beam search yet performs as accurately. With the benchmark setup in English, our parser shows an accuracy of 92.96% and a speed of 9 milliseconds per sentence, which is faster and more accurate than the previous state-of-the-art transition-based parser using beam search. It also outperforms other dependency parsers using beam search, dynamic programming, integer linear programming, etc. for languages such as Danish, Dutch, Slovene, and Swedish.