In this work, we reveal fundamental patterns that appear in individual musical careers. Such careers may go through ups and downs depending on the current market moment and release of new songs. In particular, they face hot streak periods in which high-impact bursts occur in sequence. Identifying such periods and even predicting them may help in other practical issues, which include foreseeing success and recommending artists. After modeling artists' careers as time series, we find a general trend of clustering within the most successful weeks, which justifies the applicability of the concept of hot streaks. Hence, we use a specific methodology for identifying hot streaks, whose evaluation results reveal meaningful patterns for artists of different genres. We also confirm the career peaks of artists appear and disappear progressively over time. Overall, our findings shed light on the science of musical success as we observe the temporal evolution of artists' careers and their hot streaks.