Today, a modern and interesting research area is machine learning. Another new and exciting research area is quantum computation, which is the study of the information processing tasks accomplished by practising quantum mechanical systems. This master thesis will combine both areas, and investigate quantum machine learning. Kerenidis’ and Prakash’s quantum algorithm for recommendation systems, that offered exponential speedup over the best known classical algorithms at the time, will be examined together with Tang’s classical algorithm regarding recommendation systems, which operates in time only polynomial slower than the previously mentioned algorithm. The speedup in the quantum algorithm was achieved by assuming that the algorithm had quantum access to the data structure and that the mapping to the quantum state was performed in polylog(mn). The speedup in the classical algorithm was attained by assuming that the sampling could be performed in O(logn) and O(logmn) for vectors and matrices, respectively.