We present Monte Carlo methods for multi-target tracking and data association. The methods are applicable to general nonlinear and non-Gaussian models for the target dynamics and measurement likelihood. We provide efficient solutions to two very pertinent problems: the data association problem that arises due to unlabelled measurements in the presence of clutter, and the curse of dimensionality that arises due to the increased size of the state-space associated with multiple targets. We develop a number of algorithms to achieve this. The first, which we refer to as the Monte Carlo joint probabilistic data association filter (MC-JPDAF), is a generalisation of the strategy proposed by Schulz et al. (2001) and Schulz et al. (2003). As is the case for the JPDAF, the distributions of interest are the marginal filtering distributions for each of the targets, but these are approximated with particles rather than Gaussians. We also develop two extensions to the standard particle filtering methodology for tracking multiple targets. The first, which we refer to as the sequential sampling particle filter (SSPF), samples the individual targets sequentially by utilising a factorisation of the importance weights. The second, which we refer to as the independent partition particle filter (IPPF), assumes the associations to be independent over the individual targets, leading to an efficient component-wise sampling strategy to construct new particles. We evaluate and compare the proposed methods on a challenging synthetic tracking problem.