Antihydrogen, the bound state of a positron and an antiproton, calculable from first principles, is a uniquely well suited system for searching for discrepancies between matter and antimatter that could explain the baryon asymmetry of the universe. 

The ALPHA collaboration has for more than a decade been able to trap antihydrogen atoms allowing the first detailed studies of  internal states. The ability to trap anti atoms has  evolved significantly since the first demonstration in 2010, such that we now not only trap the anti-atoms, but continuously accumulate them over many hours. Additional techniques have allowed accumulating many thousands of anti-atoms at rates of about a thousand atoms per hour. The ALPHA experiment is thus uniquely suited to continue to expand our multi pronged experiments on antihydrogen. 

These developments, together with the recent addition of laser-cooling  to the toolkit will allow us to probe the internal structure of antihydrogen to even greater precision that we've accomplished so far, and start detailed, eventually direct, comparisons with hydrogen, as well as start to extracting fundamental parameters such as the (anti)Rydberg constant, the antiproton charge radius and the (anti)Lamb shift. 

Additionally, we have only just started exploiting our vertical antihydrogen trap, something that allowed us the first observation of the influence of gravity on antimatter, and that, in particular with the enhancements above, should allow us to steadily increase the precision of these measurements to compete with measurements performed with matter systems. 

I will discuss the key techniques we have developed to have thousands of anti-atoms available for study, and discuss some of our most interesting measurements to date, focussing on the challenges and advantages of working with small samples of trapped anti-atoms when trying to elucidate their internal structure and their response to the earths gravitational field.