Many people living in low- and middle-income countries are not covered by civil registration and vital statistics systems. Consequently, household sample surveys with complex designs are often used to estimate health and population indicators. In this talk I will describe both discrete and continuous spatial models with time modeled discretely. Topics that will be touched upon include: how to account for the sampling design; the simultaneous use of both point- and area-level data; how to make adjustments for HIV epidemics; the inclusion of so-called indirect data; and covariate modeling. The modeling of under-5 mortality in Kenya is used to motivate and illustrate the issues raised. Data come from a variety of sources including Demographic and Health Surveys conducted over the period 1991–2010.