High levels of trust have been linked to a variety of benefits including the well-functioning of markets and political institutions or the ability of societies to solve public goods problems endogenously. While there is extensive literature on the macro-level determinants of trust, the micro-level processes underlying the emergence and stability of trust are not yet sufficiently understood. We address this lacuna by means of a computer model. In this paper, conditions under which trust is likely to emerge and be sustained are identified. We focus our analysis mainly on the individual characteristics of agents: their social or geographical mobility, their attitude towards others or their general uncertainty about the environment. Contrary to predictions from previous literature, we show that immobile agents are detrimental to both, the emergence and robustness of trust. Additionally, we identify a hidden link between trusting others and being trustworthy.