Penalising Brownian Paths Penalising a process is to modify its distribution with a limiting procedure thus defining a new process whose properties differ somewhat from those of the original one. We are presenting a number of examples of such penalisations in the Brownian and Bessel processes framework. The Martingale theory plays a crucial role. A general principle for penalisation emerges from these examples. In particular it is shown in the Brownian framework that a positive sigma finite measure takes a large class of penalisations into account Some penalisations of theWiener measure Feynman Kac penalisations for Brownian motion Penalisations of a Bessel process with dimension d(0 d 2) by a function of the ranked lengths of its excursions A general principle and some questions about penalisations