  We study the $\bar{B}\to D(D^*) \ell^-\bar{\nu}_{\ell}$ decays based on the
up-to-date available inputs from experiments and the lattice. First, we review
the standard model (SM) predictions of the different observables associated
with these decay channels. In the analyses, we consider new physics (NP)
effects in the channels with the heavy ($\tau$), as well as the light leptons
($\mu, e$). We have extracted $|V_{cb}|$ along with the new physics Wilson
coefficients (WCs) from the available data on light leptons; the extracted
value of $|V_{cb}|$ is $(40.3 \pm 0.5)\times 10^{-3}$. The extracted WCs are
zero consistent, but some could be of order $10^{-2}$. Also, we have done the
simultaneous analysis of the data in $\bar{B} \to D^{(*)}(\mu^-,e^-)\bar{\nu}$
alongside the inputs on $R(D^{(*)}) = \frac{\Gamma(\bar{B}\to
D^{(*)}\tau^-\bar{\nu}_{\tau})}{\Gamma(\bar{B}\to
D^{(*)}\ell^-\bar{\nu}_{\ell})}$ and the $D^*$ longitudinal polarisation
fraction $F_L^{D^*}$ in different NP scenarios and extracted $|V_{cb}|$ which
is consistent with the number mentioned above. Also, the simultaneous
explanation of $R(D^{(*)})$ and $F_L^{D^*}$ is not possible in the one-operator
scenarios. However, the two operator scenarios with $\mathcal{O}_{S_2}^{\tau} =
(\bar{q}_R b_L)(\bar{\tau}_R\nu_{\tau L})$ as one of the operators could
explain all these three measurements. Finally, we have given predictions of all
the related observables in $\bar{B} \to D^{(*)}(\tau^-,\mu^-,e^-)\bar{\nu}$
decays in the NP scenarios, which could be tested in future experiments. We
have repeated this exercise for $\bar{B} \to \pi\ell^-\bar{\nu}_{\ell}$ decays
with the light lepton and extracted $|V_{ub}|$ and the new WCs. Finally, using
all these available data for the light and heavy leptons, we have given bounds
on the couplings of the relevant SM effective field theory (SMEFT) operators
and the probable NP scale $\Lambda$.
