We study several computational problems for Boolean nested canalyzing functions (NCFs). We show that unlike general Boolean functions, there are simple algorithms for many computational problems for NCFs (e.g., equivalence & implication of NCFs, computing the probability of satisfying a given NCF, computing the sensitivity and expected sensitivity of a given NCF). The running times of these algorithms are O(n) or O(n log n), where n is the number of variables in the input function.