Intrinsic transverse parton momenta pT play an important role in the understanding of azimuthal/spin asymmetries in semi-inclusive deep-inelastic scattering (SIDIS) and the Drell-Yan process (DY). We review and update what is presently known about pT from these processes. In particular, we address the question to which extent data support the popular Gauss model for the pT -distributions. We find that the Gauss model works very well, and observe that the intrinsic transverse momenta in SIDIS and DY are compatible, which is a support for the factorization approach. As a byproduct we recover a simple but practical way of taking into account the energy dependence of pT -distributions.

We develop the minimal model of a new leading order parameterization of GPDs introduced by Shuvaev and Polyakov. The model for GPDs H and E is formulated in terms of the forward quark distributions, the Gegenbauer moments of the D-term and the forward limit of the GPD E.The model is designed primarely for small and medium-size values of x B , x B ≤ 0.2. We examined two different models of the t-dependence of the GPDs: The factorized exponential model and the non-factorized Regge-motivated model. Using our model, we successfully described the DVCS cross section measured by H1 and ZEUS, the moments of the beam-spin A

Certain exact relations among transverse momentum dependent parton distribution functions due to QCD equations of motion turn into approximate ones upon the neglect of pure twist-3 terms. On the basis of available data from HERMES we test the practical usefulness of one such "WandzuraWilczek-type approximation", namely of that connecting h, and discuss how it can be further tested by future CLAS and COMPASS data.

The violation of the so-called Lorentz invariance relations between parton distribution functions is considered in a model independent way. It is shown that these relations are not violated in a generalized Wandzura-Wilczek approximation, indicating that numerically their violation may be small.

We correct the mistaken claim made in [1,2] that the minimal model of the dual parameterization of nucleon generalized parton distributions (GPDs) gives a good, essentially model-independent description of high-energy data on deeply virtual Compton scattering (DVCS). In the implementation of the dual parameterization in [1,2], the numerical prefactor of two in front of the DVCS amplitude was missing. We show that the corrected minimal model of the dual parameterization significantly overestimates the HERA data (H1 and ZEUS) on the DVCS cross section.

A complete list of the so-called Lorentz invariance relations between parton distribution functions is given and some of their consequences are discussed, such as the Burkhardt-Cottingham sum rule. The violation of these relations is considered in a model independent way. It is shown that several Lorentz invariance relations are not violated in a generalized Wandzura-Wilczek approximation, indicating that numerically their violation may be small.

Certain exact relations among transverse momentum dependent parton distributions due to QCD equations of motion turn into approximate ones upon the neglect of pure twist-3 terms. On the basis of available data from HERMES we test the usefulness of one such "Wandzura-Wilczek-type approximation", namely of that connecting h ⊥(1) 1L to h1, and discuss how it can be further tested by future CLAS and COMPASS data. These are the proceedings of the talk given at DIS2008, London, April 2008.