ALICE (A Large Ion Collider Experiment) at the LHC has been built to study high energy Pb-Pb collisions and probe the nature of quark gluon plasma. However, delays in the LHC start-up in 2008 triggered an opportunity to develop ALICE p-p physics programme. This seminar will discuss two interesting areas of physics being probed by the ALICE experiment, neither of which involve heavy ions. The detector Central Trigger Processor (CTP), built and maintained by Birmingham, has played a crucial role in these two analysis areas. In addition, much of this work continues to be studied by Birmingham ALICE group. An early measurement of the diffractive cross sections in p-p collisions was always part of ALICE early physics programme. The first part of the seminar will address the speaker's development of this measurement and show some preliminary results. The second part will introduce one of the most exciting and uncertain areas of physics to be probed by ALICE: High Multiplicity p-p collisions. At the LHC these events may reach energy densities above that required to produce a phase transition to a Quark Gluon Plasma. The speaker's contribution to motivating and acquiring this data sample will be discussed, and the programme of work to come will be outlined.