The precise value of the neutron lifetime plays an important role in nuclear and particle physics and cosmology.  It is a key input for predicting the ratio of hydrogen to helium nuclei in the primordial universe, it is used to estimate the rate of nuclear fusion and energy production in the sun, and it can be used to search for physics beyond the Standard Model.  There exists, however, a 10-second discrepancy in the neutron lifetime as determined by two modern techniques.  By counting the decay rate of free neutrons in a beam of cold neutrons, the lifetime is 887.7 ± 2.2 s; by counting surviving ultracold neutrons stored in a material bottle, it is 878.5 ± 0.8 s.  I will describe the challenges to perform these measurements and the innovations used to overcome these challenges.