Pig survival is an economically important trait with relevant social welfare implications, thus standing out as an important selection criterion for the current pig farming system. We aimed to estimate (co)variance components for survival in different production phases in a crossbred pig population, as well as to investigate the benefit of including genomic information through single-step genomic BLUP (ssGBLUP) on the prediction accuracy of survival traits compared to results from traditional BLUP. Individual survival records on, at most, 64,894 crossbred piglets were evaluated under two multi-trait threshold models. The first model included farrowing, lactation, and combined post-weaning survival, whereas the second model included nursery and finishing survival. Direct and maternal breeding values were estimated using BLUP and ssGBLUP methods. Further, prediction accuracy, bias, and dispersion were accessed using the Linear Regression validation method. Direct heritability estimates for survival in all studied phases were low (from 0.02 to 0.08). Survival in pre-weaning phases (farrowing and lactation) was controlled by the dam and piglet additive genetic effects, although the maternal side was more important. Post-weaning phases (nursery, finishing, and the combination of both) showed the same or higher direct heritabilities compared to pre-weaning phases. The genetic correlations between survival traits within pre- and post-weaning phases were favorable and strong, but correlations between pre- and post-weaning phases were moderate. The prediction accuracy of survival traits was low, although it increased by including genomic information through ssGBLUP, compared to the prediction accuracy from BLUP. Direct and maternal breeding values were similarly accurate with BLUP, but direct breeding values benefited more from genomic information. Overall, a slight increase in bias was observed when genomic information was included, whereas dispersion of breeding values was greatly reduced. Post-weaning survival (POST) presented higher direct heritability than in the pre-weaning phases and the highest prediction accuracy among all evaluated production phases, therefore standing out as a candidate trait for improving survival. Survival is a complex trait with low heritability; however, important genetic gains can still be obtained, especially under a genomic prediction framework.