In this report we detail our work fabricating and measuring graphene quantum dots. We investigate a technique, relatively widely used in several other materials but not yet well investigated in graphene, known as Atomic Force Microscope Lithography (AFML). We then use AFML to fabricate graphene quantum dot systems. Transport measurements are carried out on our graphene quantum dots at low temperatures and high parallel magnetic fields and we try to understand the behaviour of spins in graphene. In our initial investigations into AFML we use graphene samples electrically contacted using standard electron-beam lithography. We were able to cut the graphene lattice by applying a negative voltage to the AFM tip and moving the tip across a grounded graphene surface. We have shown, by measuring the current through the AFM tip during lithography, that cutting of graphene is not current driven. Using a combination of transport measurements and scanning electron microscopy we show that , while indentations accompanied by tip current appear in the graphene lattice for a range of tip voltages, real cuts are characterized by a strong reduction of the tip current above a threshold voltage. The flexibility of the technique was then demonstrated by the fabrication, measurement, modification and re-measurement of graphene nanodevices with resolution down to 15 nm. We subsequently developed a shadow-masking technique to electrically contact graphene samples thus eliminating the use of chemical resists and the associated contamination of the graphene surface. With these pristine samples we were able to oxidise and hydrogenate the graphene using AFML. A graphene quantum dot was then fabricated using AFML oxidation. We also fabricated a graphene quantum dot using e-beam lithography in combination with oxygen plasma etching. We studied electron spin physics in these structures by J:1pplying large parallel magnetic fields at low temperatures and performing electrical transport measurements. We do not find an ordered filling sequence of spin states, which we assign to edge disorder and surface charge impurities.