Polymer nanocomposites, PNCs, based on poly(epsilon-caprolactone) (PCL) and four fillers differing in shape, namely spherical silica and Ag nanoparticles (3D, referring to the number of nanoscopic dimensions), multi-wall carbon nanotubes, CNTs, (2D), and graphene oxide, GO, nanosheets (1D), were prepared and investigated at low contents of 0.5-2.5 wt%. Scanning electron microscopy, SEM, and wide angle X-ray scattering, WAXS, were employed for morphology and crystal structure, respectively. Differential scanning calorimetry, DSC, and dielectric relaxation spectroscopy, DRS, were employed to study effects of filler on crystallization, glass transition and molecular dynamics, as well as on the amount of the rigid amorphous fraction, RAF. Except for Ag, where significant aggregation of nanoparticles was observed, SEM images indicated good dispersion of filler nano particles (fine dispersion for silica), partly confirmed also by results by the other methods employed. The glass transition temperature T-g was found to correlate well with the crystalline fraction CF in neat PCL and the PNCs, without any additional direct effect of filler. No significant effects of filler on CF were observed, in contrast to the crystallization temperature T-c, which was found to increase in the PNCs. This was discussed in terms of nucleation efficiency of the fillers, increasing in the order silica < Ag < CNT < GO which correlates better with the initial fillers' aspect ratio, however not with their specific surface area. DRS measurements show only a single alpha relaxation in the PNCs, with time scale and cooperativity (fragility) being unaffected by filler addition. The results are explained by a model, where filler particles act as additional crystallization nuclei and are embedded in the growing crystals. The CNT PNCs are characterized by low percolation threshold and high values of DC conductivity, which may be utilized in practical applications.