Laser microbeams and optical tweezers work by focusing lasers into a microscope. The energy density of a laser with a beam cross section of 1 cm2 can be condensed by almost nine orders of magnitude and focused into a volume of less than 1 femtoliter. When a comparably soft nitrogen laser pulse with 1 (mu) Joule total energy is focused to the diffraction limit, intensities above 1 Terawatt per cm2 and local temperatures above 100,000 Kelvin can be obtained. Probably a physical microplasma is generated where the laser pulse hits directly. This is the case even for comparably transparent biological objects, provided the plasma threshold can be reached. Since the heat is generated in a very small volume only, it can dissipate into the environment within a few tens of nanoseconds. This is faster than biological macromolecules can denature. Therefore, the laser microbeam interacts very locally with biological matter. In contrast to laser microbeams, optical tweezers use continuous infrared lasers of only moderate power at wavelengths with only small absorption by biological material. In such cases, the generation of heat is less prevalent and light pressure and gradient forces can be exploited to move microscopic particles. In the very inhomogeneous electric field of a highly focused laser, dielectric objects such as macromolecules, biological subcellular structures, cells or nonliving microspheres are, under suitable conditions, pulled towards the focus and are fixed there similarly as they would be fixed by micromechanical tweezers. This is true for particles with dimensions much smaller than the wavelength of the light used for trapping Rayleigh particles) as well as for particles much larger (Mie particles). Theoretical treatment of the Rayleigh particles assumes that they are linear dipoles. In contrast, many biological objects can be treated as Mie particles, where the basis for force generation is the interaction of the electromagnetic field of light with induced currents. Since Mie particles are large enough, ray optics can be used to explain the interplay of the different forces involved in optical trapping. Both, laser microbeams and optical tweezers (or synonymously 'single beam gradient laser traps') work most economically when the aperture of the microscope objective is just fully illuminated. Trapping effects are largest when the effective refractive index is between 1.1 and 1.6 -- a condition which is often satisfied with biological material.