This chapter surveys housing models using multi-dimensional panels. While there is a vast literature on housing models using two-dimensional panel data, there are few papers using multi-dimensional panels. This chapter focuses on housing models, residential mobility and location choice models derived from discrete choice theory, utilizing multi-dimensional panels. Examples include nested or hierarchical error components models, where a house is located in a street, within a block, within a city, within a county, etc. This chapter introduces some basic concepts of utility functions and discrete choice models used for hedonic functions, and residential mobility and location choices. Then it surveys some significant papers on multi-dimensional models of residential mobility and location choice. The paper concludes by surveying a few papers on dynamic housing models. It shows that both spatial and temporal dimensions in dynamic systems should be included for hedonic housing models and discrete models of residential location in a multi-dimensional framework. However, the inclusion of these multiple dimensions greatly complicates the specification and modeling of such systems.