The DØ detector underwent an upgrade to its silicon vertex detector and triggering systems during the transition from Run IIa to Run IIb to maximize its ability to fully exploit Run II at the Fermilab Tevatron. This thesis describes improvements made to the tracking and vertexing algorithms used by the high level trigger in both Run IIa and Run IIb, as well as a search for resonant di-J/ψ states using both Run I would like to thank... Rick Jesik and Gavin Davies for being my supervisors and for all their help, advice and friendship. Per Jonsson for his friendship, advice, help on Level 3 matters and for proof reading my Level 3 chapters. The Imperial College DØ group, both past and present, for all their help and advice over the years. Anyone else at Imperial or Fermilab who helped me with my thesis. My parents for sticking by me, putting me up whenever I needed a roof over my head and for encouraging me when I was down about it all. The rest of my family for always being there for me when I needed them. My friends on both sides of the Atlantic for being there for me, and distracting me from working with offerings of beer, chat and games. A special thank you goes out to Mike, Phil, Mark O and Roy for putting up with me as a flatmate over the past few years. Sneha for helping me though it all and being with me for the past 3 years. Without her help, guidance and love I don't know where I'd be right now.