Detection limits are not uncommon in biomedical research. Most approaches to handle detection limits implicitly make parametric assumptions on the distribution of data outside detection limits. We propose approaches to deal with detection limits based on widely used semiparametric ordinal regression models, cumulative probability models (CPMs). The CPM is a type of semiparametric linear transformation model that is invariant to monotonic transformation of outcomes, directly models the cumulative distribution function (CDF) and can handle mixed types of outcomes. The last property is key to handle detection limits where observations below the detection limit are discrete ordinal and those above the detection limit are continuous. With one detection limit, CPMs assign values below the detection limit as having the lowest rank. When multiple detection limits are present, we study three approaches: meta-analysis, multiple imputation, and likelihood estimation. The first two are easily applied with existing software; the latter requires minor modifications of the CPM likelihood. We illustrate the proposed approaches through simulations and application to HIV studies.