Regularity assumptions on measures are frequently made to extend results in analysis beyond the Euclidean space equipped with the Lebesgue measure. In this talk we will look at the question of existence of Ahlfors regular measures, doubling measures and measures minimizing the doubling constant. I will review some classic results providing conditions on a metric space for the existence of Ahlfors regular measures and doubling measures. Additionally, I will show that if a space admits a doubling measure, there exists a measure minimizing the doubling constant. The second talk will focus on absolute continuity between these types of measures. Both talks are based on ongoing joint work with J. Conde-Alonso and P. Tradacete.