Traditional cloud modeling methodologies apply the continuous medium approach for all thermodynamic variables, not only for the temperature and water vapor, but also for cloud condensate and precipitation. Continuous in time and space Eulerian variables used to represent cloud and precipitation particles are mass and sometimes number mixing ratios in bulk schemes and mass and/or number spectral density mixing ratios in bin schemes. Such a methodology has been the workhorse of cloud-scale modeling from its early days. However, there are challenges in applying such approaches due to numerical diffusion in the physical space and in the particle mass (or size) space for bin schemes, difficulty in representing aerosol processing by clouds, and inability to properly represent unresolved spatial scales that arguably play a significant role in the development of the particle size/mass spectra. This presentation will discuss problems with the Eulerian methodology and introduce a particle-based Lagrangian approach that is gaining popularity in cloud-scale modeling. Application of this approach to the problem of droplet spectral broadening in warm shallow clouds will illustrate key advantages of the method. Prospects of applying the Lagrangian particle-based methodology to more complex simulations involving clouds will be discussed.