Many topographic scenes exhibit complex dynamic behavior that is difficult to map, quantify, predict and understand. A terrestrial laser scanner fixed on a permanent position can be used to monitor such scenes in an automated way with centimeter to decimeter quality at ranges of up to several kilometers. Laser scanners are active sensors, and are therefore able to continue operation during night. Their independence from texture conditions ensures that in principle they provide stable range measurements for varying surface conditions. Recent years have seen a strong increase in the employment of such systems for different scientific applications in geosciences, environmental and ecological sciences, including forestry, glaciology, and geomorphology. At the same time, this employment resulted in a new type of 4D topographic data sets (3D point clouds + time) with a significant temporal dimension, as systems are now able to acquire thousands of consecutive epochs in a row. Extracting information from these 4D data sets turns out to be challenging, first, because of insufficient knowledge on error budget and correlations, and, second, because of lack of algorithms, benchmarks, and best-practice workflows. This paper provides an overview of different 4D systems for near-continuous laser scanning, and discusses systematic challenges including instability of the sensor system, meteorological and atmospheric influences, and data alignment, before discussing recently developed methods and scientific software for extracting and parameterizing changes from 4D topographic data sets, in connection to the different applications.