Ultracold trapped atoms are seen to be a promising platform for implementing quantum information processors given the long coherence times of ground-electronic hyperfine states and the ability to coherently control all degrees of freedom. In this talk I will discuss our recent work along these lines in two areas: coherent control of atomic collisions in tightly confining traps and quantum state estimation via continuous measurement. On the former, implementation of a two-atom quantum logic gate is in one-to-one correspondence with control of a molecular dimer. We explore a new trap-induced resonance and its application to this problem On the latter, we have developed a new protocol for performing full quantum-state tomography based on weak, nondestructive, continuous measurement. This has been implemented in experiments on an ensemble of cold atomic spins at the group of Prof. Poul Jessen, University of Arizona. Experimental results will be presented.