In this chapter, we consider a model of N independent random walkers, each of duration t, and each starting from the origin, on a lattice in d dimensions. We focus on two observables, namely \(D_N(t)\) and \(C_N(t)\) denoting respectively the number of distinct and common sites visited by the walkers. For large t, where the lattice random walkers converge to independent Brownian motions, we compute exactly the mean \(\langle D_N(t) \rangle \) and \(\langle C_N(t) \rangle \) . Our main interest is on the N-dependence of these quantities. While for \(\langle D_N(t) \rangle \) , the N-dependence only appears in the prefactor of the power-law growth with time, a more interesting behavior emerges for \(\langle C_N(t) \rangle \) . Even though these observables are defined for integer N and d, the results can be analytically extended to real N and real d (for example, to fractal lattices with non-integer fractal dimensions). For \(\langle C_N(t) \rangle \) , we show that there is a “phase transition” in the \((N, d)\) plane where the two critical lines \(d=2\) and \(d=d_c(N) = 2N/(N-1)\) separate three phases of the growth of \(\langle C_N(t)\rangle \) . The results are extended to the mean number of sites visited exactly by K of the N walkers. Furthermore, in \(d=1\) , the full distribution of \(D_N(t)\) and \(C_N(t)\) are computed, exploiting a mapping to the extreme value statistics. Extensions to two other models, namely N independent Brownian bridges and N independent resetting Brownian motions/bridges, are also discussed.