Optical tweezers have become an important tool in multidisciplinary research, allowing for the manipulation and study of micro- and nano-scale particles. Here, we describe the development of two optical tweezer experiments at the heart of levitated optomechanics: a Gaussian and a structured light vacuum optical tweezer. In the Gaussian experiment, we describe in detail its construction and its use to test features of stochastic motion subject to nonlinear effective forces generated via electric feedback. Next, we move to the structured light setup. Using a Spatial Light Modulator, we develop a vacuum optical tweezer with the capability of engineering arbitrary optical landscapes, including non-linearities and multi-particle traps. The experiments developed in this work pave the way to novel methods for controlling particle motion, forces and interactions, further extending the levitated optomechanics toolbox.