Dengue virus (DENV) is an endemic disease in the hot and humid low-lands of Colombia. We characterize the association of monthly series of dengue cases with indices of El Niño/Southern Oscillation (ENSO) at the tropical Pacific and local climatic variables in Colombia during the period 2007-2017 at different temporal and spatial scales. For estimation purposes, we use lagged cross-correlations (Pearson test), cross-wavelet analysis (wavelet cross spectrum, and wavelet coherence), as well as a novel nonlinear causality method, PCMCI, that allows identifying common causal drivers and links among high dimensional simultaneous and time-lagged variables. Our results evidence the strong association of DENV cases in Colombia with ENSO indices and with local temperature and rainfall. El Niño (La Niña) phenomenon is related to an increase (decrease) of dengue cases nationally and in most regions and departments, with maximum correlations occurring at shorter time lags in the Pacific and Andes regions, closer to the Pacific Ocean. This association is mainly explained by the ENSO-driven increase in temperature and decrease in rainfall, especially in the Andes and Pacific regions. The influence of ENSO is not stationary, given the reduction of DENV cases since 2005, and that local climate variables vary in space and time, which prevents to extrapolate results from one region to another. The association between DENV and ENSO varies at national and regional scales when data are disaggregated by seasons, being stronger in DJF and weaker in SON. Overall, the Pacific and Andes regions control the relationship between dengue dynamics and ENSO at national scale. Cross-wavelet analysis indicates that the ENSO-DENV relation in Colombia exhibits a strong coherence in the 12 to 16-months frequency band, which implies the frequency locking between the annual cycle and the interannual (ENSO) timescales. Results of nonlinear causality metrics reveal the complex concomitant effects of ENSO and local climate variables, while offering new insights to develop early warning systems for DENV in Colombia.