This seminar is devoted to present some recent results obtained in the field of Imprecise Previsions. We introduce the general topic evidencing the link with risk measures and we concentrate on the notions of convex and Williams' coherent imprecise previsions. These concepts are interpreted in a betting scheme, following de Finetti's approach to subjective probability. Uncertainty assessments for imprecise previsions based on those consistency conditions require that the suprema of certain random numbers, interpreted as gains, are non-negative. The extreme situation that a supremum is zero represents what is called a Weak Dutch Book (WDB). The core of this presentation aims to analyse the properties of WDBs with convex and Williams' coherent imprecise previsions. Namely, we show that WDB assessments ensure a certain `local precision' property and imply, in the agent's evaluation, some kind of `protection' against real losses. Further, these properties vary with the consistency notion we adopt, tending to vanish with the weaker one of convexity. A generalisation of the classical strict consistency notions is also discussed, in order to rule out the extreme situations caused by WDBs.