I will discuss local-global principles for two notions of semi-integral points, termed Campana points and Darmon points. In particular, I will introduce a semi-integral version of the Brauer-Manin obstruction interpolating between Manin’s classical version for rational points and the integral version developed by Colliot-Thélène and Xu. Lastly, we will apply these tools to study semi-integral points on quadric orbifolds.