Quantum field theories with defects play a ubiquitous role in theoretical physics, both for their potential applications and for the role played in the general classification of QFTs. Fixed points in the space of QFTs are represented by Conformal Field Theories with conformal defects. In this talk I will introduce a large plethora of one-dimensional defect CFTs in D=3 and study RG flows connecting them. Peculiar aspects like the existence of enriched flows and anomaly driven flows will be largely discussed. I will also consider defects at non-trivial framing and their connection with matrix model results.