This thesis presents, develops and applies new methodologies that can quantitatively probe the mechanical and viscoelastic properties of biomaterials at the nanoscale. Elastic and viscous properties are important characteristics of materials, such as many kinds of polymers and polymer solutions, colloidal solutions, but also many biological materials like cells or tissues. Very often, especially biological samples are difficult to obtain in large quantities, and measuring their mechanical properties requires the use of novel techniques that are based on local probing down to the nanoscale, like Atomic Force Microscopy (AFM) or Optical Trapping Interferometry (OTI). First we present a study on the mechanical properties of a single vimentin intermediate filament by elastically deforming it with the tip of an AFM. The resulting deflection gives a direct information on the elastic deformation of the filament itself. The bending modulus of native, non-stabilized IFs was found to be between 300 and 400 MPa. Our results together with the ones of previous works, suggest that IFs present axial sliding between their constitutive dimers, and therefore have a bending stiffness that depends on the filament length. To reduce the axial sliding between subunits, we stabilized vimentin by crosslinking with glutaraldehyde, which allowed us to conclude on a lower limit estimate of the filaments' Young's modulus. After, we present the development of a new tool for one-particle microrheology to measure locally viscoelastic properties of complex fluids with unprecedented bandwidth and resolution. Microrheology allows the characterization of very small quantities of a soft sample in a minimally invasive way, by tracking the Brownian motion of an embedded micron-sized spherical probe only driven by thermal energy. The storage modulus quantifies the elastic energy stored in the system, whereas the loss modulus is a measure for the damping due to viscosity. The method of choice to record the trajectory of the Brownian probe embedded in a complex fluid is Optical Trapping Interferometry (OTI). The optical trap has a twofold function: it ensures that the particle remains within the detector range, and it provides a light source for the position detection. By correctly calibrating the position signal of our detector, we validated a recently developed method, which is independent of any a priori assumption on the medium's viscosity and we could show that OTI can be used as a true in situ viscometer. By achieving considerable improvement in the spatio-temporal resolution of OTI, down to the nanometer and microsecond range, we could access timescales at which the inertia of the probed fluid becomes detectable. The high sensitivity of our set-up allowed us to calculate the velocity autocorrelation function (VAF) of the Brownian particle's motion at short times, where the VAF is very sensitive to the dynamics of thermal fluctuations, and hence to the nature of the structures interacting in the immediate vicinity of the probe. With such advance, we were able to track the dynamics of our Brownian microsphere, confined by a viscoelastic model polymer. Additionally to the viscoelastic modulus G*(ω), characteristic to each solution that we studied, we found that the velocity correlation function exhibits a positive or negative power-law behavior, which is strongly dependant on the solution's morphology, like polymer concentration, length, and mesh size of the network.