Preschool wheezing and childhood asthma create a heavy disease burden which is only exacerbated by the complexity of the conditions. Preschool wheezing exhibits both “curricular” and “aetiological” heterogeneity: that is, heterogeneity across patients both in the time-course of its development and in its underpinning pathological mechanisms. Since these are not fully understood, but clinical presentations across patients may nonetheless be similar, current diagnostic labels are imprecise—not mapping cleanly onto underlying disease mechanisms—and prognoses uncertain. These uncertainties also make a identifying new targets for therapeutic intervention difficult. In the past few decades, carefully designed birth cohort studies have collected “big data” on a large scale, incorporating not only a wealth of longitudinal clinical data, but also detailed information from modalities as varied as imaging, multiomics, and blood biomarkers. The profusion of big data has seen the proliferation of what we term “modern data approaches” (MDAs)—grouping together machine learning, artificial intelligence, and data science—to make sense and make use of this data. In this review, we survey applications of MDAs (with an emphasis on machine learning) in childhood wheeze and asthma, highlighting the extent of their successes in providing tools for prognosis, unpicking the curricular heterogeneity of these conditions, clarifying the limitations of current diagnostic criteria, and indicating directions of research for uncovering the etiology of the diseases underlying these conditions. Specifically, we focus on the trajectories of childhood wheeze phenotypes. Further, we provide an explainer of the nature and potential use of MDAs and emphasize the scope of what we can hope to achieve with them.