Vehicle (bike or car) sharing represents an emerging transportation scheme which may comprise an important link in the green mobility chain of smart city environments. This chapter offers a comprehensive review of algorithmic approaches for the design and management of vehicle sharing systems. Our focus is on one-way vehicle sharing systems (wherein customers are allowed to pick-up a vehicle at any location and return it to any other station) which best suits typical urban journey requirements. Along this line, we present methods dealing with the so-called asymmetric demand-offer problem (i.e. the unbalanced offer and demand of vehicles) typically experienced in one-way sharing systems which severely affects their economic viability as it implies that considerable human (and financial) resources should be engaged in relocating vehicles to satisfy customer demand. The chapter covers all planning aspects that affect the effectiveness and viability of vehicle sharing systems: the actual system design (e.g. number and location of vehicle station facilities, vehicle fleet size, vehicles distribution among stations); customer incentivisation schemes to motivate customer-based distribution of bicycles/cars (such schemes offer meaningful incentives to users so as to leave their vehicle to a station different to that originally intended and satisfy future user demand); cost-effective solutions to schedule operator-based repositioning of bicycles/cars (by employees explicitly enrolled in vehicle relocation) based on the current and future (predicted) demand patterns (operator-based and customer-based relocation may be thought as complementary methods to achieve the intended distribution of vehicles among stations).