Interval censoring and truncation arise often in cohort studies, longitudinal and sociological research. In this talk, we formulate the effects of covariates on left-truncated and mixed case interval-censored (LTIC) data without or with a cure fraction through a general class of semiparametric transformation models. We propose the conditional likelihood approach for statistical inference. For data without a cure fraction, a computationally efficient EM algorithm is proposed for obtaining the conditional maximum likelihood estimator (cMLE). For data with a cure fraction, we consider a semiparametric mixture cure model. To overcome the computational complexity due to the presence of a cure fraction, we propose a novel expression for the conditional likelihood function and then create a new complete-data likelihood function. Then, a computationally stable EM algorithm is developed for obtaining the cMLE. The large sample properties are established. The performance of our procedures are verified by intensive simulation studies and illustrated on real data sets.