We first review the impact of various sampling strategies on the estimation of discrete choice models. In particular, consistent estimates of all parameters of a multinomial logit (MNL) model, except the constants, can be obtained from an exogenous sample maximum likelihood (ESML) estimation in the presence of choice-based sampling strategies. Then, we describe the recent estimator proposed by Bierlaire, Bolduc and McFadden (2008) [The estimation of Generalized Extreme Value models from choice-based samples, Transportation Research Part B: Methodological 42(4):381-394] for the estimation of Multivariate Extreme Value models. We show that this property does not hold in general for multivariate extreme value (MEV) models. We propose a consistent ESML estimator for MEV models in this context. We then propose a new and simple weighted conditional maximum likelihood (WCML) estimator for the more general case. Contrarily to the weighted exogenous sample maximum likelihood (WESML) estimator by Manski and Lerman [Manski, C., Lerman, S., 1977. The estimation of choice probabilities from choice-based samples. Econometrica 45, 1977-1988], the new WCML estimator does not require an external knowledge of the market shares. We show that this applies also to the case where alternatives are sampled from a large choice set, and we illustrate the use of the estimator on synthetic and real data.