In the past decade, passively modelocked optically pumped vertical external cavity surface emitting lasers (OPVECSELs), sometimes referred to as semiconductor disk lasers (OP-SDLs), impressively demonstrated the potential for generating femtosecond pulses at multi-Watt average output powers with gigahertz repetition rates. Passive modelocking with a semiconductor saturable absorber mirror (SESAM) is well established and offers many advantages such as a flexible design of the parameters and low non-saturable losses. Recently, graphene has emerged as an attractive wavelength-independent alternative saturable absorber for passive modelocking in various lasers such as fiber or solid-state bulk lasers because of its unique optical properties. Here, we present and discuss the modelocked VECSELs using graphene saturable absorbers. The broadband absorption due to the linear dispersion of the Dirac electrons in graphene makes this absorber interesting for wavelength tunable ultrafast VECSELs. Such widely tunable modelocked sources are in particularly interesting for bio-medical imaging applications. We present a straightforward approach to design the optical properties of single layer graphene saturable absorber mirrors (GSAMs) suitable for passive modelocking of VECSELs. We demonstrate sub-500 fs pulses from a GSAM modelocked VECSEL. The potential for broadband wavelength tuning is confirmed by covering 46 nm in modelocked operation using three different VECSEL chips and up to 21 nm tuning in pulsed operation is achieved with one single gain chip. A linear and nonlinear optical characterization of different GSAMs with different absorption properties is discussed and can be compared to SESAMs.