Recent advances in numerical weather prediction and data assimilation, combined with the availability of high spatial, temporal and spectral resolution satellite observations and burgeoning computer power are leading to significant improvements in our ability to predict weather phenomena at higher and more appropriate resolutions. Here, we describe recent work, illustrating such improvements. High spatial and temporal (at least hourly) resolution data from sequential geostationary multispectral imagery have been used to initialise a high resolution (15km) 4-D variational assimilation (4-D Var.) system to improve tropical cyclone track prediction. The same wind data, sometimes with the addition of TOVS data from NOAA operational satellites, have also been used at higher resolution (5km) to estimate tropical cyclone intensity, demonstrating the importance of very high resolution modelling and data for this enterprise. Finally, we are using very high resolution (1km) 4-D Var. with very high spatial temporal and spectral resolution observations available from experimental advanced sounder instruments such as the High resolution Interferometer Sounder (HIS) and the NPOESS Aircraft Sounder Testbed - Interferometer (NAST - I) to examine the impact after initialisation of the improved delineation of the thermal and moisture fields by these next-generation sounders. This we believe is the first use of advanced sounder data with 4-D Var. and will assist in exploiting such data from the experimental Advanced Infrared Sounder (AIRS), the operational Infrared Atmospheric Sounding Interferometer (IASI), the Geostationary Imaging Fourier Transform Spectrometer (GIFTS) and Cross-track Interferometer Sounder (CrIS) instruments.