Quantum analogs of classical random walks have been defined in quantum information theory as a useful concept to implement algorithms. Due to interference effects, statistical properties of quantum walks can drastically differ from their classical counterparts, leading to much faster computations. In this talk, we shall discuss various statistical properties of continuous-time quantum walks on a lattice, such as: survival properties of quantum particles in the presence of traps, the growth of a quantum population in the presence of a source, and quantum return probabilities (Loschmidt echoes).